GOVERNORS 

AND  THE  GOVERNING 

OF  PRIME  MOVERS 


BY 

W.   TRINKS,   M.E. 

PROFESSOR  OF   MECHANICAL  ENGINEERING,    CARNEGIE 
INSTITUTE   OF   TECHNOLOGY,    PITTSBURGH,    PA. 


140  Illustrations 


NEW  YORK 

D.   VAN  NOSTRAND   COMPANY 

25  PARK  PLACE 

1919 


COPYRIGHT,    1919 
BY   D.   VAN  NOSTRAND  COMPANY 


THE  •  PLIMPTON  •   PRESS 
NORWOOD    •    MASS    •  U-S-A 


PREFACE 

GOVERNORS  have  been  the  play  toy  of  inventors  for  over  a 
century,  and  have  been  the  hobby  of  mathematicians  for  over 
thirty  years.  In  spite  of  these  facts,  the  knowledge  of  gover- 
nors and  of  governing  among  both  designing  and  operating 
engineers  is  very  incomplete.  There  are  several  reasons  for 
this  condition.  One  of  them  is  that  governors  do  not  cover 
a  wide  enough  field  to  warrant  a  separate  course  in  any  engineer- 
ing school.  Instruction  in  governors  is  given  in  a  scattered 
fashion.  In  courses  in  steam  engineering,  governors  for  steam 
engines  and  turbines  are  taken  up.  In  courses  on  hydraulic 
motors,  some  time  is  spent  on  governors  and  governing ;  and 
the  same  is  true  of  governors  for  internal  combustion  engines. 
Textbooks  on  prime  movers  reveal  the  same  condition  of  affairs. 
Everywhere  that  which  is  apparent  on  the  surface  is  reprinted, 
but  nowhere  (with  very  few  exceptions)  does  the  investigation 
go  below  the  surface. 

The  present  book  aims  to  fill  this  gap.  As  far  as  I  am  aware, 
there  exists  to-day  no  other  book  of  any  consequence  on  gov- 
ernors and  governing  in  the  English  language.  There  are  books 
in  French,  German,  and  Swedish,  but  they  are  of  little  use  to 
English-speaking  engineers. 

The  present  volume  is  a  book  of  essentials  and  principles. 
Practice  changes ;  there  are  fashions  in  engineering  almost 
as  changeable  as  those  in  women's  clothes ;  but  engineering 
principles  do  not  change.  For  that  reason,  I  have  tried  to  dig 
out  that  which  is  essential,  and  to  present  it  in  such  a  manner 
that  the  reader  is  put  in  a  position  to  judge  existing  and  future 
types  of  governors  as  well  as  the  properties  of  prime  movers 
with  regard  to  regulation.  In  consequence,  the  book  contains 
not  a  single  catalogue  picture.  Every  drawing  was  especially 
prepared  to  show  in  a  diagrammatic  manner  that  which  is 
important,  with  the  intentional  omission  of  everything  else. 

The  book  contains  more  than  I  give  my  students  in  the 


A   1 


vi  PREFACE 

classroom.  Students,  as  a  rule,  do  not  know  what  their  life- 
work  will  be  in  later  years.  While  in  school,  they  can  be  given 
only  the  "meat  of  the  essentials."  They  are,  however,  anxious 
to  know  of  a  source  out  of  which  they  can  fill  the  gaps  which 
their  necessarily  brief  instruction  at  school  has  left.  Never- 
theless, the  book  by  no  means  covers  the  whole  subject  of 
governing  of  prime  movers.  Many  extremely  interesting  sub- 
jects were  omitted,  for  two  reasons  :  First,  it  was  necessary 
to  keep  the  price  of  the  book  within  such  limits  as  not  to  make 
its  purchase  a  burden.  Second,  it  was  desirable  to  restrict  the 
mathematical  side  of  the  book  to  a  level  which  undergraduates 
can  master,  so  that  the  reader  may  be  spared  the  troubles  of 
intellectual  indigestion. 

It  is,  however,  planned  to  follow  this  book,  later  on,  with 
another  one  on  the  subjects  of  "  dynamics  and  design  of  modern 
governors  for  prime  movers,"  which  will  be  primarily  intended 
for  those  engineers  who  make  governors  and  governing  a  life 
study.  In  that  book  many  subjects  can  be  taken  up  which  are 
clearly  beyond  the  limits  of  the  present  volume.  The  foot- 
notes referring  back  to  the  preface  indicate  some  of  the  subjects 
which  are  to  be  taken  up  in  that  volume.  In  addition,  the 
other  book  will  take  up  the  effect  of  water  inertia  in  hydraulic 
turbines  and  the  governing  of  prime  movers  driving  alternators 
in  parallel.  The  present  book  was  started  in  the  spring  of 
1913.  Lack  of  spare  time  and  necessity  for  original  work  in 
the  preparation  of  this  book  have  delayed  its  completion  until 
now.  By  the  term  "original  work"  I  mean  that  practically 
all  of  the  theories  advanced  by  me  were  tried  out  practically. 
Some  of  the  tests  were  made  in  the  Mechanical  Engineering 
Laboratory  of  the  Carnegie  Institute  of  Technology,  but  most 
of  the  trials  were  made  in  the  field,  in  the  attempt  to  help  those 
who  had  trouble  with  regulation. 

College  graduates  will  have  no  trouble  with  the  mathe- 
matical part.  Operating  engineers  who  have  not  had  the  good 
fortune  of  college  training  should  likewise  have  no  trouble,  if 
they  turn  to  the  elementary  derivations  given  in  the  appendix. 
By  comparison,  they  will  realize  that  the  differential  calculus 
is  a  wonderful  short-cut. 


PREFACE 


VII 


Like  other  books  dealing  with  a  specialty  of  applied  me- 
chanics, the  present  book  must  contain,  for  some  readers, 
much  that  is  known,  and  must  occasionally  pass  over  the 
heads  of  others.  It  is  impossible  to  pitch  the  scale  right  for 
everybody. 

The  bookmark,  containing  all  symbols,  will,  I  hope,  be  of 
assistance. 

For  those  who  wish  to  go  more  deeply  into  the  subject  of 
governing,  and  who  have  library  facilities,  the  bibliography 
will  be  valuable.  It  was  prepared  by  the  Carnegie  Library  of 
Pittsburgh.  The  librarians  worked  faithfully  on  this  task.  I 
herewith  thank  them  for  their  cooperation. 

W.  THINKS 

PITTSBURGH,  MAY,  1919. 


CONTENTS 

PAGE 

PREFACE v 

LIST  OF  SYMBOLS xiii 

INTRODUCTION xv 

CHAPTER  I 

GENERAL  STATEMENTS 1 

1.  Purposes  of  Governors 1 

2.  Forces  Used  in  Governing 2 

CHAPTER  II 

THE  DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR 4 

1.  Strength  of  Centrifugal  Governors 4 

2.  Regulating  Force  of  Tangential  Inertia 8 

3.  Work  Capacity  of  Centrifugal  Governors 14 

4.  Detention  by  Friction 15 

5.  Overcoming  a  Passive  Resistance 19 

CHAPTER  III 

THE    CENTRIFUGAL    GOVERNOR    AS    A    MEASURING    INSTRUMENT    (SPEED 

COUNTER) 23 

1.  Equilibrium  Speed,  Static  Fluctuation,  Stability 23 

2.  Characteristic  Curves 25 

3.  Constituent  Parts  of  Characteristics 34 

4.  Influence  of  Shape  of  Centrifugal  Weights 40 

CHAPTER  IV 

PROMPTNESS  AND  TRAVERSING  TIME 45 

CHAPTER  V 

ADJUSTMENT  OF  EQUILIBRIUM  SPEED 49 

ix 


x  CONTENTS 

CHAPTER  VI 

PAGE 

SHAFT  GOVERNORS 61 

1.  Forces  Acting  in  Shaft  Governors 61 

2.  Centrifugal  Moment , 63 

3.  Moment  Caused  by  Inertia  of  Valve  Gear  Parts 64 

4.  Moment  Caused  by  Friction  of  Valve  Gear  Parts 66 

5.  Moment  Caused  by  Friction  of  Eccentrics 67 

6.  Spring  Moment 69 

CHAPTER  VII 

NATURAL  PERIOD  OF  VIBRATION  OF  GOVERNORS 77 

CHAPTER  VIII 

EFFECTS  OF  OUTSIDE  FORCES  IMPRESSED  UPON  GOVERNORS 81 

1.  Resistibility 81 

2.  Cyclical  Vibrations  of  Governors 85 

CHAPTER  IX 

INTERACTION  BETWEEN  GOVERNOR  AND  PRIME  MOVER 95 

1.  Action  of  Governors  Regulating  Prime  Movers 95 

2.  Limiting  Case 98 

3.  The  Influence  of  Tangential  Inertia  upon  Stability  of  Regulation 113 

4.  Damping  of  Governor  Vibrations  by  Solid  Friction 117 

5.  Greatest  Speed  Fluctuation  in  Direct-control  Governing 128 

CHAPTER  X 

DISCARDED  TYPES  OF  SPEED  GOVERNORS 139 

CHAPTER  XI 

RATE-OF-FLOW  GOVERNORS 148 

CHAPTER  XII 

PRESSURE  GOVERNORS 153 


CONTENTS  xi 
CHAPTER  XIII 

PAGE 

RELAY  GOVERNING 170 

1.  Reasons  for  the  Use  of  Relay  Governors,  and  Forces  Acting  upon  Them  170 

2.  Mechanisms  of  Relay  Governors 173 

3.  Work  Capacity  of  Relay  Governors 184 

4.  Speed  Fluctuations  in  Relay  Governing 186 

CHAPTER  XIV 

GOVERNOR  TROUBLES  AND  THEIR  REMEDIES 195 

1.  Regulation  Not  Close  Enough 195 

2.  Racing 195 

3.  Speed  Fluctuation  too  Great  when  Load  Changes 201 

4.  Vibration  of  Governor 202 

5.  Rapid  Wear  of  Joints 203 

6.  Machine  Design  Troubles 203 

CHAPTER  XV 

SELF-REGULATING  FEATURES  OP  PRIME  MOVERS 204 

APPENDIX 209 

BIBLIOGRAPHY 219 

INDEX  .  231 


LIST  OF  SYMBOLS 

To  accompany 

"  Governors  and  the  Governing  of  Prime  Movers." 
By  Prof.  W.  Trinks 


A  ....  Governor  travel,  or  displacement.  V .  . 

B  Distance. 

C Centrifugal  force.  W . . 

D .  .  . »  Small  difference;;  X .  . 

E  ....Energy.  Z  .. 

F  . .. . Force     at     collar    to    overcome  a  . . 

governor  friction.  b  . . 
G  ....  Area. 

H .  .  . .  Radius  of  gyration.  d  . . 

I  . . . .  Moment  of  inertia  1  mass  x  e   .  . 
J  ... .  Moment  of  inertia  /  (radius)2 

K Constant.  /  .  . 

L  . . .  .  Lever  arm.  g  . . 

M Moment.  h  . . 

P  —  Strength  of  governor;  also  i   .  . 

Restoring  force  per  unit  displace-  j   .  . 

ment.  k  . . 

Q  . . .  .  Weight  or  force.  I   .  . 

R  —  Force  on  governor  collar  to  over-  m .  . 

come  valve  friction  only.  n  . . 

S  .. . . Spring  force.  p  . . 
T  . . . .  Special  time. 

Tb . . .  .  Brake-resistance  traversing  time.  q  . . 

Tf Time  required  to  fill  volume  of  r  .  . 

container.     (In   pressure    gov-  s  .  . 

erning.)  t   .  . 

Tg Traversing  time  of  governor.  u  . . 

Z\. . . .  Starting  time  o£anjertia  mass.  v  .  . 

Tn. . . .  Time  of  one*complete  vibration  of  w  . . 

a  governor.    (Natural  period  of 

vibration.)  x  . . 

Tr Relay  traversing  time. 

Ts Starting  time  of  plrime  mover.  y  . . 

U.  .  . . Relative  speed  deviation.  z  . . 


.  .Volume;  also 

Volume  flowing  in  unit  time. 
. .  Weight. 

. .  Relative  governor  deviation. 
. .  Relative  load  change. 
. .  Angular  acceleration. 
. .  Radial     travel     of      centrifug; 

weights. 
. .  Differential. 
. .  Base  of  Naperian  logarithms;  also 

Efficiency. 

.  .Friction  coefficient. 
. .  Gravity  acceleration. 
. .  Height  or  space  dimensions. 
. .  Angle. 
. .  Angle. 
. .  Angle. 
. .  Length. 
.  .  Mass. 

. .  Revolutions  per  minute. 
.  .Static  fluctuation;   also 

Pressure. 

. .  Detention  by  governor  friction. 
.  .Radius. 
.  .Space. 
.  .Time. 

. .  Angular  velocity. 
.  .  Linear  velocity. 
. .  Angular     velocity     of     auxiliary 

vector. 
.  .Abscissa;  also 

Unknown  quantity. 
. .  Ordinate. 
..Stability;  also 

Root  of  an  equation. 


LIST  OF  SYMBOLS 

To  accompany  "  Governors  and  Governing  of  Prime  Movers."    By  Prof.  W.  Trinks 


A ....  Governor  travel,  or  displacement. 

B  . . . .  Distance. 

C Centrifugal  force. 

D .  .  .  .  Small  difference. 

E  Energy. 

F  . . . .  Force  at  collar  to  overcome 
governor  friction. 

G  ....Area. 

H .  .  . .  Radius  of  gyration. 

7 Moment  of  inertia  1  mass  x 

J  ... .  Moment  of  inertia  j  (radius)2 

K .  . . .  Constant. 

L  . . .  .  Lever  arm. 

M Moment. 

P Strength  of  governor;  also 

Restoring  force  per  unit  displace- 
ment. 

Q  . . .  .  Weight  or  force. 

R Force  on  governor  collar  to  over- 
come valve  friction  only. 

S  . . . .  Spring  force. 

T  ....  Special  time. 

Tb . . . .  Brake-resistance  traversing  time. 

Tf Time  required  to  fill  volume  of 

container.     (In   pressure    gov- 
erning.) 

Tg Traversing  time  of  governor. 

T». . . .  Starting  time  of  inertia  mass. 

Tn . . . .  Time  of  one  complete  vibration  of 
a  governor.  (Natural  -period  of 
vibration.) 

Tr Relay  traversing  time. 

Ts . . . .  Starting  time  of  prime  mover. 

U .  .  . .  Relative  speed  deviation. 


V .  .  .  .Volume;  also 

Volume  flowing  in  unit  time. 

W Weight. 

X .  .  . .  Relative  governor  deviation. 
Z  —  Relative  load  change. 

a Angular  acceleration. 

b Radial      travel     of     centrifugal 

weights. 

d Differential. 

e   ....  Base  of  Naperian  logarithms;  also 

Efficiency. 
/  .  . . .  Friction  coefficient. 

g Gravity  acceleration. 

h Height  or  space  dimensions. 

i   .  . . .  Angle. 

j  Angle. 

k Angle. 

I   ....  Length. 
m .  .  .  .  Mass. 

n Revolutions  per  minute. 

p Static  fluctuation;   also 

Pressure. 

q  Detention  by  governor  friction. 

r  .  . . .  Radius. 
s  .  . .  .Space. 

t Time. 

u  ....  Angular  velocity. 
v  .  .  . .  Linear  velocity. 

w Angular    velocity    of    auxiliary 

vector. 
x  . . .  .Abscissa;  also 

Unknown  quantity. 
y  . . . .  Ordinate. 
z   . .  ..Stability;  also 

Root  of  an  equation. 


xm 


GOVERNORS 

AND    THE 

GOVERNING   OF   PRIME   MOVERS 

INTRODUCTION 

THE  title  of  the  present  book,  viz.  "  Governors,  and  the 
Governing  of  Prime  Movers/7  clearly  indicates  that  the  study 
of  governing  comprises  two 
distinct  parts,  one  being  a 
treatment  of  the  governor  as 
a  mechanism,  and  the  other 
being  an  investigation  of  the 
interaction  between  the 
governor  and  the  prime 
mover. 

That  this  division  is  not 
only  logical  but  is  also 
historical  will  be  realized 
from  a  brief  reciting  of  the 
history  of  governing  for  con- 
stant speed.  In  the  his- 
torical sketch  which  now 
follows,  many  of  the  dates 
are  approximate  only  ;  they 
must  necessarily  be  so,  be- 
cause the  development  of 
correct  engineering  princi- 
ples and  the  adoption  of  FIG.  1 
improved  apparatus  are  very 

slow  processes.     Besides,  the  periods  of  development  overlap 
in  different  countries. 

Early  mechanical  engineers,  that  is  to  say  the  builders  of 
water  wheels,  wind  mills,  and  steam  engines,  studied  governors 

XV 


xvi  INTRODUCTION 

as  separate  mechanisms  and  developed  their  theories  with 
utter  disregard  of  the  reciprocal  action  of  governor  and  prime 
mover.  This  condition  existed,  with  very  few  exceptions, 
from  the  time  of  James  Watt  (who  invented  the  centrifugal 
governor  in  the  year  1784)  to  almost  1880.  The  Watt  governor 
(Fig.  1)  adjusts  for  higher  and  higher  rotative  speeds  as  the 
revolving  balls  move  away  from  the  axis  of  revolution.  As 
might  be  expected,  this  property  of  the  governor  was  con- 
sidered a  drawback,  but  not  until  the  middle  of  the  nineteenth 
century  were  any  steps  taken  to  remedy  the  defect.  The 
search  for  the  isochronous,  or  "astatic"  governor,  which 
would  regulate  for  the  same  speed  at  all  loads,  began.  Thus 
we  find  the  "parabolic  governor"  which,  when  operated  on 
a  test  block,  is  truly  isochronous,  introduced  about  1850.  For 
the  same  purpose  governors  with  crossed  arms  were  invented 
from  1860  to  1870  by  different  engineers  (Kley,  Farcot,  Head) 
in  different  countries.  With  the  same  end  in  view,  the  high 
speed  governor  of  Porter,  Proell's  inverted  governor,  and  the 
oblong  weight  "Cosine"  governor  appeared  in  the  two  decades 
from  1860  to  1880.  The  same  period  gave  birth  to  many  other 
forms  of  governors,  for  instance  the  dynamometric  (or  load-) 
types  (see  Chapter  X),  which  attempted  to  adjust  the  supply 
of  energy  directly  by  means  of  the  demand  for  it. 

All  of  these  types  of  governor  have  disappeared  for  reasons 
explained  in  Chapter  X.  A  new  period  dawned  from  about 
1870  to  about  1882,  when  governors  were  extensively  applied 
to  horizontal  shafts  (Porter's  marine  governor,  Hartnell's 
crankshaft  governor).  Gravity  could  not,  in  these  adaptations, 
furnish  the  controlling  centripetal  force,  and  springs  had  to 
be  employed.  The  action  of  spring-loaded  governors  was  so 
superior  to  that  of  weight-loaded  governors  that  inventors 
placed  many  new  types  of  spring-loaded  governors  on  the 
market  from  1880  to  1895  (about).  The  term  "inventors" 
is  used  purposely  instead  of  "engineers,"  because  the  vast 
majority  of  the  designs  of  that  period  reveal  inventive  ability 
rather  than  good  engineering  judgment.  From  about  1890 
on,  the  influence  of  electrical  power  generation  helped  to 
perfect  mechanical  governors  in  the  same  measure  in  which 


INTRODUCTION  xvii 

it  has  helped  to  perfect  all  types  of  mechanical  equipment  of 
power  plants. 

While  inventors  were  busy  bringing  out  new  types  of 
governors,  usually  without  any  knowledge  of  the  mutual 
relations  between  prime  mover  and  governor,  these  very  rela- 
tions were  studied  by  two  widely  different  types  of  men,  namely 
the  operating  engineer,  and  the  mathematician.  The  former 
found  that  the  wonderful  " isochronous"  governors,  such  as 
the  parabolic  governor,  the  cosine  governor,  and  many  others, 
were  worthless  because  they  caused  perpetual  hunting  and 
racing.  Oil  gag-pots  were  found  to  be  necessary  ;  and  fre- 
quently stabilizing  springs  were  concealed  in  them ;  but  with 
all  this  practical  progress,  the  theoretical  foundation  or  proof 
for  the  exasperating  behavior  remained  unknown  to  engineers, 
or  else  was  not  understood  by  them. 

At  the  other  end  of  the  line,  mathematicians  studied  the 
interaction  between  governor  and  prime  mover.  Starting 
about  1840  with  the  regulation  of  astronomical  telescopes, 
British  and  French  scientists  gradually  extended  their  investi- 
gations to  the  governing  of  prime  movers.  But  their  researches 
were  of  no  benefit  to  the  practical  engineer,  because  they  were 
published  in  the  proceedings  of  astronomical  or  philosophic 
societies.  More  attention  was  paid  to  the  very  ingenious 
theoretical  solution  of  the  governing  problem  by  the  Russian 
engineer  Wischnegradsky,  which  was  published  in  1876  and 
1877  in  Russian,  French,  and  German.  Although  his  publica- 
tions are  the  foundation  upon  which  modern  theories  of  govern- 
ing are  built,  they  were  scoffed  at  by  engineers,  partly  because 
they  failed  to  explain  some  of  the  plainly  visible  phenomena  of 
regulation,  and  partly  because  they  were  clad  in  very  mathe- 
matical form.  Wischnegradsky's  work,  unfortunately,  was 
given  very  little  or  no  appreciation  in  English-speaking  countries. 

From  about  1890  to  the  outbreak  of  the  European  war, 
French  and  German  engineering  literature  (including  Switzer- 
land and  Austria)  have  been  very  active  on  the  mutual  relations 
between  governor  and  prime  mover,  while  British  and 
American  engineers  either  took  no  interest  in  the  theoretical 
development,  or  else  were  too  busily  engaged  with  practical 


xviii  INTRODUCTION 

experimenting  to  pay  attention  to  theory.  Of  course  there 
are  exceptions,  the  most  prominent  of  which  is  the  large 
number  of  American  contributions  to  the  development  of  the 
theory  of  the  action  of  long  pipe  lines  on  the  governing  of 
hydraulic  turbines. 

Even  to-day,  the  subject  of  governing,  that  is  to  say,  the 
interaction  between  the  governor  and  prime  mover,  is  very 
little  understood  by  engineers.  In  the  1905  edition  of  the 
widely  used  English  book  on  Dynamics  by  Routh,  this  state- 
ment is  made:  "The  defect  of  a  governor  is,  therefore,  that 
it  acts  too  quickly,  and  thus  produces  considerable  oscilla- 
tions of  speed  in  the  engine."  A  similar  statement  was  made 
by  Swinburne,  the  well-known  English  engineer,  in  "Indus- 
tries," 1890.  As  a  matter  of  fact,  the  principal  progress  in 
the  improvement  of  regulation  has  consisted  in  making  gov- 
ernors act  more  quickly.  It  is  evident  that  there  is  need  for 
clearing  up  this  subject,  if  even  the  best  of  us  can  go  astray 
on  it.  In  consequence,  considerable  emphasis  is  placed  on  the 
problem  of  governing  in  the  present  book. 

To-day  the  theories  of  governors  as  mechanisms  and  of 
governing  have  reached  a  certain  stage  of  development  beyond 
which  it  is  scarcely  necessary  to  go,  for  practical  purposes. 
However,  we  must  admit  that  present  theory  is  by  no  means 
complete  ;  on  the  contrary,  it  is  far  from  it.  But  additional 
information  can  only  be  gained  by  a  combination  of  experi- 
ment and  mathematics  which  is  at  present  beyond  the  reach 
of  most  practical  engineers. 


CHAPTER   I 

GENERAL    STATEMENTS 

1.  Purpose  of  Governors.  —  Governors  are  used  to  auto- 
matically adapt  the  output  of  prime  movers  to  the  demand. 

Governors  are  superfluous,  whenever  the  torque  resisting 
the  motion  of  a  prime  mover  increases  considerably  with  the 
speed  and  depends  solely  upon  the  speed.  This  is  the  case  in 
marine  service,  where  the  resistance  grows  approximately  as 
the  square  of  the  speed,  and  in  locomotive  service.  It  is  also 
the  case  in  some  classes  of  pumping  machinery.  If  the  resist- 
ing torque  grows  with  the  speed,  and  is  not  subject  to  varia- 
tions except  those  caused  by  the  speed  of  the  prime  mover, 
then  the  supply  of  energy  can  be  adjusted  by  hand,  because 
there  can  be  only  one  speed  for  a  given  supply  of  energy. 
Hand  adjustment  is  usually  practiced  in  the  cases  mentioned, 
which  means  that  under  such  circumstances  the  purpose  of 
the  governor  is  narrowed  down  to  that  of  a  safety  speed-limit 
which  prevents  running  away  of  the  engine  or  turbine,  if  the 
resisting  torque  should  be  suddenly  removed.  If,  however, 
the  torque  is  repeatedly  removed,  as  it  occurs,  when  the  pro- 
peller comes  near  the  surface  in  a  high  sea,  the  governor  ap- 
proaches the  more  normal  type  mentioned  below  under  (1). 

Usually  some  factor  in  the  operation  of  the  prime  mover 
is  to  be  kept  constant,  or  nearly  constant,  while  other  factors 
vary.  Thus  we  find  : 

(1)  Constant  speed,  variable  torque. 

(2)  Constant    (average    per    revolution)    torque,    variable 
speed. 

(3)  Constant  quantity  of  one  factor  of  the  output,  with 
variation  of  both  speed  and  torque. 

As  examples  of  heading  (1)  may  be  cited  engines  or  turbines 
operating  electric  generators,  driving  lineshafts,  etc.  In  elec- 
trical power  transmission,  turning  lights  on  or  off,  switching 

i 


2       .aOYOR§tADBE  GOVERNING  OF  PRIME  MOVERS 


motors  on  and  off,  etc.,  varies  the  resisting  torque,  while  the 
requirements  of  constant  number  of  cycles  and  of  constant 
voltage  necessitate  keeping  the  speed  of  the  prime  mover 
constant.  Under  (2)  come  pumping  machines  maintaining  a 
constant  pressure,  but  varying  the  output  by  adjustment  of 
rotary  speed.  An  example  is  found  in  air  compressors  supply- 
ing air  to  tools  in  mines.  In  spite  of  variable  demand  for  air, 
the  pressure  must  be  kept  constant.  Under  (3)  come  centrif- 
ugal pumping  machines  maintaining  a  constant  flow  of  fluid 
against  a  variable  pressure.  The  relation  between  pressure, 
speed,  and  torque  is  determined  in  this  case  by  the  character- 
istics of  the  prime  mover  and  of  the  pump. 

It  is  evident  that  purposes  differing  as  widely  as  those  men- 
tioned under  the  three  headings  require  different  types  of 
governing  devices. 

2.  Forces  Used  in  Governing.  —  Every  governor  per- 
forms two  separate  functions,  namely  : 

(a)  that  of  measuring  the  quantity  which  it  is  to  keep 
practically  constant, 

(6)  that  of  varying  the  supply  of  energy  to  the  prime  mover 
so  that  the  just  mentioned  quantity  is  kept  constant. 

A  governor,  then,  is  both  a  measuring  device  and  a  motor. 
In  conformity  with  the  purposes  mentioned  in  the  preceding 
paragraph,  governors  measure 

(1)  angular  velocity 

(2)  the  intensity  factor  generated  by  the   machine  which 

is  driven  by  the  prime  mover 

(3)  the  extensity  factor  of  this  energy. 

Under  heading  (2)  come  pressure  and  electromotive  force. 
Under  heading  (3)  come  rate  of  flow  and  electric  current. 

In  the  evolution  of  the  art  of  governing,  many  principles 
have  been  used,  but  one  by  one  they  were  discarded  (see 
Chapter  X)  ,  until  to-day  practically  one  principle  is  left,  namely 
this  :  A  force  is  produced  by  the  quantity  to  be  measured  ; 
it  is  balanced  by  an  external  known  force  such  as  is  derived 
from  springs  or  weights.  Any  change  in  the  quantity  to  be 
measured  unbalances  the  system.  As  soon  as  the  unbalanced 
force  is  strong  enough  to  overcome  resistance,  it  constitutes 


GENERAL  STATEMENTS  3 

the  motive  force  for  adjusting  the  supply  of  energy.  The 
principle  in  question  has  been  pronounced  defective  and  faulty, 
because,  to  cause  the  governor  to  act,  it  necessitates  a  change 
in  the  quantity  to  be  kept  constant.  However,  the  change 
can  be  made  exceedingly  small ;  and  the  principle  has  the  very 
great  advantage  that  governing  is  accomplished  regardless  of 
the  source  of  the  disturbance.  This  important  theorem  will 
be  fully  explained  later  on. 

If  the  just  mentioned  force  acts  directly  on  the  mechanism 
which  adjusts  the  supply  of  energy,  the  governor  is  said  to  be 
direct  acting,  or  to  be  a  " direct  control"  governor. 

If  the  unbalanced  force  is  too  feeble  to  overcome  the  re- 
sistance of  the  energy  controlling  mechanism,  it  becomes 
necessary  to  call  upon  an  auxiliary  energy  for  motive  power, 
which  energy  is  released  and  controlled  by  the  unbalanced 
governor  force.  If  this  is  done,  the  governor  is  called  a  relay 
governor.  Motor  forces  used  in  relay  governing  are  most 
varied.  The  principal  ones  among  them  are  : 

(1)  Mechanical  force  derived  from  the  motion  of  the  prime 
mover. 

(2)  Fluid  pressure  acting  on  a  piston. 

(3)  Electromagnetic  attraction. 

All  governors  of  the  present  period  have  certain  general 
features  in  common,  such  as  strength,  work  capacity,  detention 
by  friction,  behavior  in  overcoming  a  passive  resistance,  prompt- 
ness, resistibility  and  others.  While,  for  that  reason,  it  might 
be  logical  to  discuss  these  properties  in  a  general  way,  a  different 
course  will  be  followed  for  the  sake  of  clearness.  More  than 
90%  of  the  total  number  of  governors  in  operation  are  of  the 
centrifugal  type,  so  that  it  seems  advisable  to  develop  the 
general  properties  of  governors  with  particular  reference  to 
the  centrifugal  governor.  Transfer  of  the  conclusions  to  other 
types  of  governors  will  not  be  difficult,  once  the  theory  of  the 
centrifugal  governor  is  clearly  understood. 

References  to  Bibliography  at  end  of  book:  35,  36,  63. 


CHAPTER   II 

THE  DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR 

1.  Strength  of  Centrifugal  Governors.  —  When  acting 
as  a  motor  (that  is,  when  shifting  the  power  controlling  mechan- 
ism to  a  new  position),  the  governor  does  work.  The  latter 


Spring  balance  ^ 

Indicates  Strength  P 


Suspension 
points. 


Centrf 
mass. 


Sleeve  or  collar. 


FIG.  2 

can  be  expressed  as  force  times  distance  or  as  moment  times 
angle.  As  will  be  explained  later  on,  the  force  or  moment  used 
in  the  act  of  regulating  are  functions  of  that  force  P  (or  moment 

4 


THE   DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR  5 

MP)   which   are  required  to  move  the  governor,   when  not 
rotating,  against  centripetal  force. 

The  place  of  action  of  this  force  (resp.  moment)  is  shown 
in  Figs.  2  and  4  ;  the  former  represents  a  spindle  type  of 
governor  which  shifts  the  power  controlling  mechanism  by 
up  and  down 
motion  of  the 
sleeve  or  collar 

(1)  ;  Fig.  4  rep-  1. 

resents  a  shaft 
governor  which 
controls  the 
supply  of  energy 
by  shifting  the  zc 
center  of  the 
eccentric  along 
the  arc  (l)-(2). 
The  strength  P 
can  be  determined  experimentally  by  lifting  up  the  sleeve  of 
the  governor  and  reading  the  force  on  a  spring  balance,  as 
sketched  in  Fig.  2.  The  true  strength  is  obtained,  if  friction 
is  eliminated  by  vibration,  for  instance  by  rapping  the 
governor  with  a  wooden  hammer.  In  German  treatises  on 
governors  and  in  translations  of  such  treatises  the  force  P  of 
the  not-rotating  governor  is  called  the  " energy"  of  the 
governor.  This  term  is  obviously  misleading.  It  has  been 
replaced  in  the  present  book  by  the  term  "  strength." 

The  "  strength"  of  the  governor  is  closely  related  to  that 
radial  or  centrifugal  force  2C,  Fig.  2,  which  is  necessary  to 
balance  the  frictionless  governor,  or  to  keep  the  governor 
sleeve  floating.  Let  ds  be  a  small  displacement  of  the  sleeve 
(say  3%  of  the  total  working  travel  of  the  sleeve),  then  the 
rigidity  of  the  mechanism  results  in  a  radial  displacement  dr 
of  the  centrifugal  weights.  The  graphical  construction  of  dr 
for  a  given  value  of  ds  is  shown  in  Fig.  2.  From  the  theory  of 
virtual  displacements,  we  have 


FIG.  3 


P  ds  =  2  C  dr 


(1) 


GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


In  equation  (1),  P  is  the  strength  of  the  governor,  and  C  is 
that  radial  (and  in  Fig.  2  horizontal)  force  which,  if  applied 
at  the  mass  center  of  each  centrifugal  weight,  just  balances  P 
in  the  frictionless  governor.  If  a  spring  balance  were  attached 

to  each  centrifugal 
weight,  and  if  it  were 
pulled  radially  outward, 
then  it  would  indicate 
the  force  C  (provided,  of 
course,  that  the  spring 
balance  correctly  indi- 
cates horizontal  forces, 
and  that  friction  is  elimi- 
nated). In  operation  of 
the  governor,  the  force 
C  is  furnished  by  radial 
inertia  and  is  called  cen- 
trifugal force.  From 
equation  (1)  follows  the 
important  fact  that  the 
strength  is  proportional 
to  the  centrifugal  force,  so  long  as  ds/dr  remains  constant.1 

In  the  case  of  the  shaft  governor,  there  is  no  well-defined, 
constant  direction  for  the  action  of  the  regulating  force,  so 
that  the  regulating  force  is  replaced  by  a  regulating  moment. 
But  the  "  strength  moment "  coincides  with  the  moment  exerted 
by  the  spring  (spring  moment).  Hence  there  exists  no  reason 
for  the  use  of  the  term  "  strength  moment."  In  shaft  governors 


FIG.  4 


1  The  relation  between  strength  and  centrifugal  force  can  be  illustrated  by  the 
aid  of  a  simple  example.  In  Fig.  3,  let  two  weights  W  be  suspended  by  massless 
rods  as  shown.  Then  the  weights  W  can  be  kept  from  dropping  either  by  two  hori- 
zontal forces  \G  or  by  a  vertical  force  P.  From  a  triangle  of  forces  \C  =  W;  we 

p 
may  also  resolve  P  into  two  inclined  forces  P'  =  — -i=  ;  take  moments  about  the  sus- 

p 

pension  point  (1),  then  —p.  I  =  W  I  \/2,  or  P  =  2W.  Hence  C  =  P  in  this  case.    This 

V2 

result  can  be  had  directly  from  the  principle  of  virtual  displacements.  Move  the 
weights  through  the  small  distance  db,  then  radial  travel  dr  of  force  C  and  axial 
travel  ds  of  force  P  are  alike;  hence  P  =  C,  since  P  ds  =  C  dr. 


THE  DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR  7 

the  centrifugal  moment  and  the  spring  moment  do  not  coin- 
cide, because  there  are  many  forces  impressed  upon  the  ec- 
centric. This  feature  is  dealt  with  explicitly  in  the  chapter 
on  shaft  governors. 

To  exert  its  full  strength,  a  centrifugal  governor  must 
slow  down  from  its  normal  speed  to  a  dead  stop.  In  practice 
only  very  small  speed  fluctuations  are  allowed,  so  that  only 
a  small  part  of  the  strength  can  be  exerted.  To  find  this  frac- 
tion, call  u  the  normal  angular  velocity  of  the  governor  spindle, 
and  du  a  small  change  of  that  angular  velocity.  From  me- 
chanics it  is  well  known  that  centrifugal  force  C  =  mru2, 
where  m  =  mass  of  the  revolving  body,  and  r  =  radius  to 
mass  center  of  that  body.  Corrections  to  this  equation  on 
account  of  oblong  shape  of  revolving  body  are  given  in  para- 
graph 4  of  Chapter  III.  For  symmetrical  shapes,  such  as  a 
sphere  or  a  cylinder,  no  correction  is  needed.  Let  the  governor 
be  prevented  from  moving  its  sleeve,  while  the  speed  changes 
the  amount  du;  then  r  remains  constant ;  and  since  m  natu- 
rally is  constant,  C  and  u  are  the  only  variables.  Hence  the 
change  of  centrifugal  force  is  by  differentiation.1 

dC=2mrudu=2mru2  du/u  =  2  C  du/u (2) 

This  equation  is  true  for  infinitesimally  small  changes  of 
u  only,  but  is  in  practice  accurate  enough  even  for  du  =  10  % 
of  u.  The  following  equation  is  then  approximately  correct: 

DC  =  2  C  Du/u (3) 

where  Du/u  is  the  relative  speed  change.  Du  is  not  an  infinitesi- 
mal quantity,  but  a  small  fraction  of  u,  of  the  magnitude  which 
is  usually  allowed  in  practice.  The  governor  was  in  internal 
equilibrium  before  the  speed  change  ;  it  is  not  in  internal  equilib- 
rium after  the  speed  change.  If  the  governor  is  frictionless, 
the  radial  force  DC  produces  an  axial  force  DP  =  DC  dr/ds 
at  the  sleeve  ;  this  force  is  known  as  the  regulating  force  for 
the  relative  speed  change  Du/u.  By  substitution  we  obtain 

DP  =  4  C  —  T  =  2P  Du/u W 

u    as 

(for  2  weights!) 

1  For  an  elementary  derivation  see  Appendix,  p.  209. 


8        GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


Rotation 


From  this  equation  it  follows  that  the  regulating  force  is 
proportional  to  the  strength  of  the  governor  and  to  the  rela- 
tive speed  change.  It  equals  the  product  of  4C  (where  C  is 
the  centrifugal  force  of  each  of  the  two  weights),  Du/u  (which 

is  the  relative  speed 
change)  and  dr/ds 
(which  is  the  ratio  of 
radial  travel  of  centrif- 
ugal weight  and  of 
axial  travel  of  sleeve 
for  a  small  displace- 
ment of  the  governor) . 
To  express  this  re- 
lation  in  figures, 
imagine  a  governor 
with  a  strength  of  250 
pounds ;  let  the  gov- 
ernor be  in  equilibrium 
at  300  revolutions  per 
minute,  and  let  the 
speed  drop  to  297  revo- 
lutions per  minute. 
Then  the  governor  will 
exert  a  force  of  2  X  .01  X  250  =  5  pounds  on  its  collar  tending 
toward  a  new  equilibrium  position.  In  this  case  the  regulating 
force  equals  five  pounds. 

It  should  be  noted  that  the  available  regulating  force 
becomes  smaller  as  the  governor  approaches  its  new  position. 
This  feature  will  be  explained  in  detail  later  on. 

The  corresponding  moment  equation  for  shaft  governors 
is  never  written,  because  the  pulsating  moments  continually 
impressed  upon  a  governor  of  that  type  upset  any  elementary 
theory  which  might  be  founded  upon  a  "  regulating  moment." 

References  to  Bibliography  at  end  of  book:    1,  24,  35,  36,  37,  52,  53,  73. 

2.  Regulating    Force    Due    to    Tangential    Inertia.  —  In 

Fig.  5  is  shown  an  eccentric  with  center  (1),  mounted  loose 
on  a  shaft  the  center  of  which  is  (2).  Let  the  valve  gear  be 
so  arranged  that  clockwise  relative  rotation  of  the  eccentric 


FIG.  5 


THE  DIRECT-CONTROL  GOVERNOR  AS  A   MOTOR  9 

reduces  the  supply  of  power,  and  let  the  shaft  rotate  in  the 
direction  indicated  by  the  arrow  at  the  top  of  the  illustration. 
The  details  of  the  valve  gear  are  at  present  immaterial.  A 
concrete  example  of  variation  of  power  by  rotation  of  an 
eccentric  is  furnished  by  the  well  known  "  Buckeye "  steam 
engine.  If  the  demand  for  power  is  suddenly  increased,  an 
angular  retardation,  or  negative  angular  acceleration  a  occurs, 
the  magnitude  of  which  depends  upon  the  dimensions  of  the 
prime  mover,  upon  the  change  of  load  and  upon  the  moment 
of  inertia  "J"  of  the  rotating  mass  connected  to  the  eccen- 
tric. If  the  latter  does  not  rotate  relatively  to  the  shaft,  a 
moment  (a  J)  is  exerted  upon  the  eccentric,  tending  to  rotate 
it.  Regulating  forces  or  moments  caused  by  tangential  inertia 
differ  from  those  produced  by  radial  inertia  (centrifugal  force), 
inasmuch  as  the  latter  has  to  wait  for  the  speed  to  change 
before  it  becomes  effective  (see  equation  3  on  page  7), 
whereas  tangential  inertia  becomes  effective  at  the  instant 
when  the  change  of  load  occurs. 

From  this  fact  it  might  appear  at  first  thought  as  if  tan- 
gential inertia  should  be  universally  used  for  speed  governing 
purposes.  Many  such  attempts  have  been  made ;  but  the 
survival  of  the  fittest  has  eliminated  most  of  them  and  has 
limited  the  application  of  tangential  inertia  almost  entirely 
to  shaft  governors.  The  theoretical  reasons  underlying  this 
decision  of  practice  are  partly  given  in  this  chapter,  and  will 
partly  be  explained  in  paragraph  6  of  Chapter  VI  and  para- 
graph 3  of  Chapter  IX,  because  they  depend  upon  the  dynamics 
of  regulation. 

The  principle  of  using  tangential  inertia  as  a  regulating 
agent  differs  from  the  principle  enunciated  in  paragraph  2  of 
Chapter  I  and  forms  the  principal  exception  to  that  principle. 
It  is  discussed  in  the  present  place  to  show  the  difficulties 
which  even  the  slightest  departure  from  the  general  principle 
introduces. 

The  governor  shown  in  Fig.  5  is  worthless,  because  it  does 
not  adjust  any  particular  speed.  It  simply  tries  to  keep  con- 
stant the  accidental  speed  at  which  the  prime  mover  happens 
to  be  operating.  A  prime  mover  provided  with  such  a  governor 


10      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

could  not  be  started,  because  the  resulting  acceleration  would 
shut  off  the  power,  unless  the  inertia  wheel  were  kept  out  of 
action  by  some  other  agency.  Furthermore,  the  inertia  wheel 
is  inactive  for  very  gradual  changes  of  speed,  because  the 
acceleration  "a"  is  then  very  small  and  usually  insufficient 
to  overcome  friction  resistance.  With  gradual  change  of  load, 
the  speed  can  thus  rise  or  fall,  until  either  equilibrium  is  at- 
tained by  means  other  than  the  governing  equipment,  or  else 
the  prime  mover  is  wrecked  or  stalled. 

These  reasons  make  it  necessary  to  combine  tangential 
inertia  (if  it  is  to  be  used  for  governing  purposes)  with  centrif- 
ugal force  and,  speaking  in 
very  general  terms,  to  make 
the  latter  so  strong  that  it 
wm*  compensate  for  the 
above  mentioned  shortcom- 
ings of  tangential  inertia. 
Such  a  combination  may 
be  effected  either  by  the 
use  of  separate  inertia  and 
centrifugal  masses,  or  by 
the  use  of  a  mass  which 
serves  both  purposes. 

In  illustrations  6  to  9 
both  of  these  arrangements 
FIG.  6  are  shown.    Figures  6  and 

7  show  spindle  governors; 

8  and  9  show  shaft  governors.  The  illustrations  are  purely 
diagrammatic  and  are  intended  to  bring  out  principles  only, 
with  omission  of  all  design  details.  In  Figures  6  and  8  each 
mass  is  utilized  for  both  radial  and  tangential  inertia  action; 
in  Figures  7  and  9  separate  masses  are  provided  for  the  two 
effects. 

On  mass  (1)  of  Fig.  6  the  action  of  tangential  inertia  is 
indicated  for  a  sudden  increase  of  speed  (reduction  of  load); 
on  mass  (2)  the  action  of  centrifugal  force  is  indicated.  Evi- 
dently the  two  forces  act  in  the  same  sense  for  the  direction 
of  rotation  marked  in  the  illustration. 


THE  DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR 


11 


From  Fig.  8  it  is  plain  that  the  action  of  centrifugal  force 
on  mass  center  (1)  turns  clockwise  about  suspension  point  (2), 
so  that  an  increase  of  speed  likewise  produces  clockwise  rota- 
tion. A  study  of  the  illustration  also  brings  out  the  fact  that 
for  the  indicated  direction  of  rotation,  tangential  inertia  acts 


FIG.  7 

in  the  same  sense.     Point    (3)   represents  the  center  of  the 
eccentric  which  operates  the  valve  gear. 

In  Fig.  7,  (1)  is  an  inertia  ring,  loosely  mounted  on  the 
revolving  spindle.  (2)  and  (2)  are  the  centrifugal  masses 
which  are  guided  radially  by  bell  cranks  (3).  The  two  mass 
systems  are  connected  by  a  pinion  and  two  racks.  In  this  type 


12      GOVERNORS   AND  THE  GOVERNING  OF   PRIME   MOVERS 


of  governor  the  complete  separation  of  the  two  force  systems 

is  very  distinct. 

In  Fig.  9,  (1)  is  the  inertia  mass,  and  (2)  is  the  centrifugal 

mass.  They  swing  about  the 
points  (4)  and  (5)  which  are 
fixed  in  the  revolving  wheel. 
Point  (3)  is  again  the  center  of 
the  eccentric.  In  this  type  the 
two  force  actions  are  not  en- 
tirely separated,  because  each 
mass  is  partly  subjected  to  the 
not  intended  force. 

From  page  9  we  remember 
that  the  regulating  moment  is 
(a/).  This  expression  may 


FIG. 


be  misconstrued  into 
the  belief  that  the 
moment  could  be  in- 
creased  to  any 
desired  amount  by 
a  corresponding 
increase  of  J.  Such 
a  conclusion  would 
be  wrong,  because, 
as  J  grows,  a  be- 
comes less  for  a 
given  change  of  load. 
For,  as  long  as  the 
wheel  does  not  yet 
shift  the  eccentric,  it 
acts  the  same  as  if  it 


FIG.  9 


were  keyed  to  the  shaft,  or  as  if  it  were  part  of  the  flywheel. 


THE   DIRECT-CONTROL  GOVERNOR  AS  A   MOTOR  '  13 

And  for  a  given  change  of  load  the  rate  of  change  of  speed  is 
the  smaller,  the  greater  the  inertia  of  the  flywheel. 

The  arrangement  of  Fig.  8  is  frequently  used;  for  this 
reason  an  expression  will  now  be  developed  for  the  regulating 
moment  produced  by  governors  of  this  type. 

In  the  diagram  (Fig.  10),  (1)  is  the  center  of  the  rotating 
shaft,  (2)  is  the  pivot  about  which  the  inertia  weight  with 
mass  center  (3) 
swings.  Let  the 
system  start  from 
rest  with  an  angular 
acceleration  a,  and 
let  joint  (2)  be 
inactive,  that  is 
rigid.  For  conven- 
ience of  calculating, 
the  motion  of  the 
mass  may  be  re- 
solved into  a  curvi- 
linear translation  of 
the  mass  center 
from  (3)  to  (4),  and 
into  a  rotation  of 
the  mass  from  (5)  to  (6)  about  its  center  (4).  The  total  inertia 
moment  must  be  the  sum  of  the  inertia  moments  due  to  transla- 
tion and  rotation.  The  moment  about  point  (2)  (which  latter 
becomes  point  (6)  at  the  end  of  the  interval  of  time  under  con- 
sideration) then  is 

M  =  mr  a  L  +  J  a  =  a(mr  L  +  J), 

where  J  is  the  moment  of  inertia  of  the  pendulum  about  its 
own  mass  center  (3)  and  where  L  is  the  lever  arm  of  the  trans- 
latory  inertia  force  mru  about  the  pivot  (2). 

It  is  evident  that  the  regulating  force  or  moment  is  made 
smaller  by  the  regulating  motion  of  the  governor;  but  that 
does  not  matter.  For,  as  long  as  the  governor  moves  toward 
its  new  configuration,  its  purpose  is  served,  even  though  the 
available  regulating  force  be  lessened  thereby.  It  should  be 


Moss  m 


FIG.  10 


14      GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

noted  that  the  regulating  force  of  a  centrifugal  governor  is 
likewise  reduced  as  it  approaches  its  correct  position. 

The  regulating  moment  mr  a  L  +  J  a  is  the  only  moment 
which  interests  us.  Other  forces  act,  but  they  are  not  of  vital 
influence.  They  will,  however,  be  mentioned.  Since,  in  prac- 
tice, the  whole  system  rotates,  while  the  acceleration  occurs, 
centrifugal  forces  must  be  added,  and  if  the  inertia  mass  swings 
about  pivot  (#),  compound  centrifugal  forces  must  be  added 
(the  latter  are  known  as  Coriolis'  forces,  see  paragraph  4  of 
Chapter  IX).  While  the  centrifugal  forces  have  a  moment, 
the  compound  centrifugal  forces  lie  in  the  direction  (#)-(#) 
and  have  no  moment.  However,  they  produce  friction. 

Study  of  Fig.  8  teaches  that  in  this  form  of  governor  the 
moment  due  to  m  r  L  a  is  quite  small  compared  to  the  moment 
caused  by  J  a.  It  should  be  understood  that  the  moment 
M  =  a  (m  r  L  +  J)  refers  to  an  ideal  f rictionless  governor  only. 

The  theory  of  the  action  of  tangential  inertia  in  the  inter- 
action between  governor  and  prime  mover  will  be  found  in 
paragraph  3  of  Chapter  IX,  which  deals  with  the  dynamics  of 
regulation. 

References  to  Bibliography  at  end  of  book:  2,  33,  36,  73. 

3.  Work  Capacity  of  Centrifugal  Governors. —  If  the  sleeve 
of  a  non-rotating  centrifugal  governor  of  the  spindle  type  be 
raised  through  its  working  travel  s,  the  work  P  s  is  done, 
where  P  is  the  average  strength  of  the  governor.  This  work 

may  also  be   expressed  as    I  P  ds,  where  P  is  the  variable 

Jo 

strength  of  the  governor. 

Obviously  this  expression  represents  the  greatest  amount 
of  work  which  can  be  done  by  the  governor  as  a  motor,  unless 
speeds  considerably  in .  excess  of  the  normal  are  considered. 

Hence,  the  expression    I  P  ds  is  called  the  work  capacity  of 

the  governor.    Its  numerical  value  is  usually  given  in  governor 
catalogues. 

Again  it  is  obvious  that  for  purposes  of  regulation  only  a 
small  part  of  the  work  capacity  can  be  utilized,  because  a 
speed  change  of  100%  cannot  be  allowed  in  practice. 


THE   DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR  15 

Before  the  available  part  of  the  work  capacity  can  be 
found,  the  influence  of  friction  in  governor  and  valve  gear 
must  be  studied. 

References  to  Bibliography  at  end  of  book:  36,  37,  73. 

4.  Detention  by  Friction.  —  If  a  spindle  governor  be  run  at 
such  a  speed  that  it  is  floating,  touching  neither  the  upper 
nor  the  lower  stop,  the  speed  can  be  varied  between  the  limits 
uh  and  ut,  while  the  governor  sleeve  remains  motionless.  Any 
speed  higher  than  uh  raises  the  governor,  any  speed  lower 
than  HI  lowers  it.  The  ratio 


q 


has  received  various  names,  namely  "  detention  by  friction," 
"  sluggishness,"  "time  lag,"  "  insensibility,"  or  "degree  of  in- 
sensibility." In  the  present  book  the  name  "detention  by 
friction"  will  be  adopted.  This  quantity  depends  upon 

(1)  the  design  of  the  governor, 

(2)  its  lubrication, 

(3)  the  vibration  to  which  it  is  subjected,  while  the  speed 
changes, 

(4)  the   forces   transmitted   to   the   governor   through   the 
sleeve. 

Taking  up  these  items  in  the  order  given,  we  find  that  in 
a  governor  of  the  type  shown  in  Fig.  2  or  in  Fig.  6,  centrifugal 
and  centripetal  forces  are  balanced  by  forces  passing  through 
numerous  joints,  each  of  which  produces  friction,  whereas  in 
the  type  shown  in  Fig.  7  these  forces  are  balanced  directly 
without  the  interposition  of  joints.  Consequently  the  former 
type  has,  under  otherwise  equal  conditions,  more  friction  than 
the  latter,  and  shows  more  detention  due  to  friction.  The 
friction  can  be  somewhat  reduced  by  the  use  of  knife  edges. 

Item  2,  lubrication,  certainly  affects  friction.  Governors 
may  be  so  designed  that  the  joints  are  always  submerged  in 
oil.  Such  a  design  furnishes  the  only  case  in  which  the  degree 
of  lubrication  is  definitely  known.  In  all  other  cases  it  is 
uncertain. 

In  many  governor  catalogues  the  detention  due  to  friction 


16      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

is  given  on  the  basis  of  a  certain  coefficient  of  friction  and  of 
absence  of  vibration.  The  calculations  made  for  determining 
the  detention  are  more  or  less  arbitrary  and  of  doubtful  value, 
unless  all  are  based  on  the  same  coefficient  of  friction.  In 
that  case  the  figures  afford  a  comparison  which  can  be  used  to 
advantage. 

The  immediate  purpose  of  any  such  calculation  is  to  find 
between  what  limits  the  force  C  in  Fig.  2  can  be  varied  without 
moving  the  mechanism.  The  solution  of  this  problem  is  a 
matter  of  applied  mechanics.  It  may  be  effected  by  graphic 


Governor  Position 


statics  or  by  taking  moments,  or  by  the  principle  of  virtual 
displacements.  In  the  appendix  two  numerical  examples  are 
given. 

Under  average  conditions  the  detention  varies  for  different 
types  of  governors  and  for  various  degrees  of  lubrication  from 
\%  up  to  4 %.  The  detention  q  usually  varies  for  different 
positions  of  one  and  the  same  governor. 

Item  3,  vibration,  considerably  affects  detention,  as  may 
be  judged  from  the  following  fact  which  proves  that  vibrations 
always  reduce  and  often  eliminate  friction.  Objects  lying 
quietly  on  an  apparently  horizontal  table  march  off  promptly, 
if  the  table  is  rapped  by  a  vibrating  instrument,  such  as  a 
pneumatic  hammer,  riveter,  etc.  In  the  same  manner  a  governor 
subject  to  vibrations  loses  the  detention  by  friction  in  various 


THE  DIRECT-CONTROL   GOVERNOR  AS  A  MOTOR 


17 


degrees.  To  prove  this  fact,  the  author  artificially  produced 
vibrations  in  an  ordinary  Watt  type  spindle  governor  by 
atttaching  an  unbalanced  revolving  weight  to  its  collar. 
Figs.  11  and  12  show  speed  and  position  of  the  governor 
plotted  against  time.  Fig.  11  was  taken  with  the  weight  at 
rest,  and  Fig.  12  was  taken  with  the  weight  revolving  at  high 
speed. 

It  will  be  observed  that  Fig.  11  shows  the  peculiar  jaggy 
motion  of  detention,  whereas  in  Fig.  12  practically  every 
trace  of  detention  is  eliminated.  Note  the  practically  straight 
line,  which  represents  motion  without  detention.  Incidentally 


\       A  /5peed  "8! 


Time 


FIG.  12 


it  will  be  noticed  that  the  speed  of  the  governor  varied 
cyclically  during  the  test,  whereas  the  speed  appeared  to  the 
observer  to  be  uniform.  Circumstances  of  this  sort  make 
even  the  experimental  determination  of  the  detention  by 
friction  difficult. 

Influence  4,  namely  that  of  forces  transmitted  through  the 
governor  sleeve,  will  be  considered  in  Chapter  VIII. 

In  spite  of  the  fact  that  vibrations,  variation  of  lubrication, 
and  other  circumstances  make  the  detention  by  friction  an 
uncertain  quantity,  we  must  admit  that  there  are  cases  where 
the  theory  of  the  detention  by  friction  is  well  applicable  (see 


18      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


next  paragraph).     In  such  cases  the  following  equations  are 
useful : 


detention  q  =  - 


uh  —  HI  uh2  —  uf  mr  Uh*  —  mr 


uh 


\      2 
dr          dr 

Ch  -  Ci       'h  ds       /l  ds      Ph-  PI 


(uh  +  ui\ 


2C 


ds 


or  approximately 


2(P  -  Pf)      P-  P^      F 


2P 


P          P 


In  these  equations  Ch,  C,  and  Cz  are  centrifugal  forces  for 
high,  average,  and  low  speed,  covering  the  range  over  which 

the  governor  is  detained 
by  friction;  P  is  the 
strength  of  the  governor 
for  the  position  under 
consideration.  Evidently 
a  governor  can  have  only 
one  value  for  its  strength 
at  a  given  position ;  hence 
the  expressions  Ph  —  P 
and  P  —  PI  must  mean 
additional  axial  forces  at 
the  sleeve,  sufficient  to 
overcome  the  internal 
friction  of  the  governor. 
For  this  reason  the  said 
values  have  been  denoted 
by  the  letter  F. 

If  q  has  been  deter- 
mined by  calculation,  the 
equivalent  friction  force 
F  can  be  found  from  the 
final  equation  q  =  F  /P. 

References  to  Bibliography  at  end  of  book:  36,  73. 


FIG.  13 


THE   DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR 


19 


Equal 


5.  Overcoming  a  Passive  Resistance  by  a  Centrifugal 
Governor. — When  moving  the  throttle  valves  of  steam  turbines, 
or  well-balanced  throttle  valves  of  engines,  governors  overcome 
" passive  resistance,"  that  is  to  say  a  resistance  which  exerts 
no  vibratory  or  shaking  force  upon  the  governor. 

In  order  to  determine  the  influence  of  a  passive  resistance 
upon  a  governor,  imagine  the  latter  to  be  replaced  by  a  spring 
balance  at  point  (1), 
Fig.  13.  It  should  be 
understood  that  the 
linkage  between  the 
governor  and  the  valve 
gear  must  be  so  arranged 
as  to  vary  the  energy 
supply  to  the  prime  -xd=-zo* 
mover  from  zero  to  its 
maximum  value,  while 
the  governor  sleeve 
passes  through  its  range 
of  travel.  Let  the  forces 

which  are  measured  in 

,    ,  FIG.  14 

moving  the  spring  bal- 
ance up  and  down  be  Xu  and  —  Xd  respectively. 

V"      J_     V 

~T    -A  d 


Then 


=  R  is  the  passive  resistance  of  the  valve 


gear,  that  is  to  say  a  force  which  resists  motion  either  way  and 
affects  the  motor  part  of  the  governor.     On  the  other  hand, 

V       V 

-  is  a  force  which  does  not  affect  the  motor  part  of  the 

governor,  but  only  the  speed  counter  part.1    Even  if  the  pas- 
sive resistance  of  the  valve  gear  were  entirely  eliminated  by 

1  To  make  these  relations  clear,  imagine  the  valve  resistance  replaced  by  the 
f rictional  resistance  of  a  spring  load  acting  on  a  heavy  block  (/),  Fig.  14.  If  the 
f fictional  resistance  is  15  pounds,  then  the  forces  at  the  governor  collar  necessary  t$> 
move  the  weight  are  10  and  —20  pounds  as  indicated.  The  resistance  of  15  pounds 
concerns  the  motor  part  of  the  governor,  and  the  constant  force  of  5  pounds  reduces 
the  equilibrium  speed  of  the  governor. 


20      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

V  V 

vibrations,  -  -  would  still  act  and  would  be  noticed  by 

the  speed  counting  properties  of  the  governor.  See  below  in 
paragraph  1  of  Chapter  III. 

R  is  then  the  force  which  the  governor  must  overcome  in 
order  to  shift  the  valve  gear,  provided  that  the  governor  itself 
is  free  from  friction;  but  from  the  preceding  paragraph  it  is 
known  that  most  governors  have  friction  and  must,  for  this 
reason,  overcome  an  additional  force  F  (equivalent  friction 
force).  Hence  the  governor  must  exert  a  force  R  +  F  to  move 
the  valve  gear.  This  fact  is  mathematically  expressed  by  the 
following  equations  : 

(1)  R  =  D  P=  2  P  —  see  (4)  on  page  7. 

u 

(2)  F  =  q  P  =  2  P  —  see  page  18. 

u 

The  2  in  the  second  equation  comes  from  the  definition  for 
q;  the  value  of  q  covers  the  whole  detention  above  and  below 

normal  speed,  so  that  q  =  -        -  is  equal  to  twice  the  relative 

u 

speed  change  which  is  necessary  to  overcome  the  internal  re- 
sistance F;  DIU  is  that  speed  change  which  is  necessary  to 
overcome  the  external  resistance  R.  Addition  of  equations 
(1)  and  (2)  furnishes 

I  u  +  Z>2  u 


R  +  F  = 2P 


u 


From  this  follows  the  total  speed  change  which  is  necessary 
to  overcome  both  resistances  : 

R  +  F         ufR 


Evidently  the  desirable  effect  of  making  the  total  speed 
change  small  can  partly  be  obtained  by  the  increase  of  the 
strength  P;  partly  only,  because  F/P  is  a  constant  for  a  given 
type  of  governor  and  provides  a  lower  limit  for  the  speed 
change,  no  matter  how  strong  the  governor  might  be. 


THE  DIRECT-CONTROL  GOVERNOR  AS  A  MOTOR  21 

According  to  the  theory  just  presented,  it  would  be  impos- 
sible to  obtain  close  regulation,  unless  the  internal  friction  of 
the  governor  were  reduced  to  almost  nothing.  This  viewpoint 
is  strongly  emphasized  in  catalogues  advertising  governors 
with  small  internal  friction.  On  the  other  hand,  everyday 
experience  proves  'that  in  many  cases  close  regulation  is 
obtained  even  with  governors  having  considerable  internal 
friction.  As  may  be  surmised,  vibratory  forces  from  various 
sources  partially  or  wholly  eliminate  friction  in  these  cases. 
See  also  chapters  on  resistibility  and  on  shaft  governors. 

In  other  cases,  where  vibratory  forces  are  either  absent, 
or  quite  small  compared  to  the  passive  friction  resistance, 
nothing  remains  but  the  use  of  strong  governors  with  small 
internal  friction  (see  chapter  on  relay  governing).  In  that 
case  it  is  advisable  to  investigate  the  required  speed  change 
for  two  positions  of  the  governor  and  valve  gear,  because  the 
strength  of  the  governor  and  the  resistance  of  the  valve  gear 
usually  vary  from  position  to  position. 

In  practice  the  difficulty  arises  that  neither  the  frictional 
passive  resistance  can  be  exactly  predetermined  nor  the  help- 
ing vibratory  force  is  definitely  known,  so  that  judgment  is 
required  in  the  selection  of  a  governor.  In  the  regulation  of 
gas  engines  working  with  dirty  gas  (producer  gas,  blast  furnace 
gas,  coke  oven  gas)  exceptionally  great  strength  of  governors 
is  needed,  because  the  regulating  valves  which  are  operated 
by  the  governor  gradually  clog  with  dirt,  and  stick.  Weak 
governors  require  too  frequent  cleaning  of  the  regulating 
valves. 

Insufficient  strength  of  governors  coupled  with  absence  of 
vibratory  forces  can  easily  be  recognized  from  the  speed  varia- 
tions which  occur  even  with  the  smallest  and  most  gradual 
changes  of  load  on  the  prime  mover. 

To  make  matters  even  clearer,  an  example  will  be  given. 
Let  the  passive  resistance  of  the  governor  rig  be  10  pounds, 
measured  at  the  governor  collar.  Let  q,  the  detention  by 
internal  governor  friction,  be  equal  to  1|  %•  Let  it  be  stipu- 
lated that  the  total  speed  variation  in  overcoming  the  valve 
resistance  with  gradual  changes  of  load  must  not  exceed  2%. 


22      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

What  strength  P  of  the  governor  is  necessary  to  meet  these 
requirements?  For  a  solution  we  will  write  equation  3  in  this 
form: 

_  D  U  R    f  u-   u    r>  R 

—  q  =  — ,  from  which  P  =  — — — 


u 

Z q 

u 

By  substitution, 


References  to  Bibliography  at  end  of  book:  36,  73. 


CHAPTER   III 

THE    CENTRIFUGAL   GOVERNOR   AS    A   MEASURING 
INSTRUMENT   (SPEED    COUNTER) 

1.   Equilibrium   Speed,    Static    Fluctuation    and   Stability. 

—  If,  in  a  prime  mover,  the  resisting  torque  is  reduced,  while 
the  torque  which  is  produced  either  remains  constant  or  is 
not  reduced  as  much  as  the  resisting  torque,  the  liberated 
excess  energy  is  converted  into  kinetic  energy,  that  is  to  say, 
the  speed  grows.  For  the  sake  of  stability,  the  governor  must 
be  so  arranged  that  the  increase  of  speed  causes  it  to  move 
the  torque-controlling  mechanism  toward  the  no-load  posi- 
tion. The  inverse  series  of  events  has  to  be  gone  through,  if 
the  load  is  increased. 

As  mentioned  in  paragraph  1  of  Chapter  I,  the  purpose  of 
speed  governing  is  to  keep  the  speed  constant  in  spite  of  varia- 
tions of  torque.  It  will  be  shown  in  this  paragraph  and  in 
paragraph  2  of  Chapter  IX  that  centrifugal  governors  must 
have  a  higher  equilibrium  speed  (at  least  temporarily)  at  no 
load  than  at  full  load,  in  order  to  make  use  of  the  principle 
enunciated  at  the  beginning  of  the  present  paragraph. 

The  smaller  the  speed  variation,  the  better  the  governing. 
In  consequence,  several  measures  of  the  closeness  of  regula- 
tion have  been  introduced;  most  important  among  them  is  the 
term  " fluctuation "  or  "static  fluctuation,"  which  means 

uu  —  Ud  .  ,1N 

p  = — (1) 

J(t*«  +  ud) 

In  this  equation  uu  means  that  speed  at  which  the  governor 
is  in  equilibrium  in  its  uppermost  (or  equivalent)  position,  and 
ud  means  that  speed  at  which  the  governor  is  in  equilibrium 
when  in  its  lowest  position.  The  term  "is  in  equilibrium" 
means  that  the  governor  is  floating  between  centrifugal  and 
centripetal  forces,  with  friction  eliminated.  Uppermost  and 
lowermost  position  refer  to  no  load  and  to  full-load  positions. 

23 


24       GOVERNORS  AND   THE   GOVERNING  OF   PRIME   MOVERS 


The  terms  " outermost"  and  " innermost"  are  more   correct, 
but  are  seldom  used. 

If  a  prime  mover  could  be  made  (which  it  cannot)  to  always 
run  at  a  speed  proportional^to  the  equilibrium  speed  of  the 
governor,  a  small  value  of  p  would  mean  close  regulation,  and 
p  =  0  would  represent  the  ideal  case  of  constant  speed  regula- 
tion. A  governor  of  this  description  (p  =  0)  is  called 
isochronous. 

In  speaking  of  static  fluctuation,  governor  manufacturers 
usually  assume  that  the  whole  range  of  the  travel  of  the  governor 
collar  is  utilized  for  varying  the  torque  produced  by  the  prime 

mover,  from  zero  to  its 
maximum  value.  If  that 
condition  does  not  exist, 
that  is  to  say,  if  a  fraction 
of  the  travel  of  the  collar 
varies  the  torque  through 
its  complete  range,  the 
static  fluctuation  of  the 
governor,  as  given  in  the 
governor  catalogues,  re- 
mains the  same,  but  the 
effect  upon  the  prime 
mover  is  different  and  is 
equivalent  to  a  reduction  of  static  fluctuation,  or  to  an  increase 
of  sensitiveness. 

A  governor  with  a  small  static  fluctuation  is  spoken  of  as  a 
" sensitive"  governor,  so  that  the  sensitiveness  of  a  governor 
is  closely  related  to  the  value  1  /p. 

An  example  will  illustrate  these  statements.  In  Fig.  15 
the  numbers  represent  the  equilibrium  speeds  for  certain  posi- 
tions of  the  governor  collar.  If  the  total  available  travel  of 
the  latter  be  utilized  in  governing,  the  static  fluctuation  is 

-  =  10  %.     If,  on  the  other  hand,  the  position  marked 
luu 

102 J  rev./niin.  is  the  no-load  position,  and  the  one  marked  97^ 
is  the  full-load  position,  then  -  — -  =  5%  is  the  static 


FIG.  15 


fluctuation. 


100 


THE   GOVERNOR  AS  A   MEASURING  INSTRUMENT  25 

The  mistake  is  often  made  to  assume  that  an  engine  or 
turbine  will  work  with  close  regulation,  because  it  has  been 
equipped  with  a  sensitive  governor,  which,  as  before  stated, 
means  a  governor  with  small  static  fluctuation.  Such  an 
assumption  is  wrong.  The  sensitiveness  of  a  governor  gives 
no  guarantee  for  close  regulation,  and  too  great  a  sensitiveness 
will  often  make  it  impossible  to  obtain  close  regulation.  For 
detail  discussion  of  the  causes  underlying  these  facts  see 
paragraph  2  of  Chapter  IX. 

The  static  fluctuation  of  a  governor  is  related  to  its  sta- 
bility, which  means  its  ability  to  return  to  the  position  of 
equilibrium  after  it  has  been  displaced  from  that  position. 
For  a  judicious  discussion  of  this  point,  knowledge  of  the 
"  characteristic  "  of  a  governor  is  necessary.  See  the  following 
paragraph. 

References  to  Bibliography  at  end  of  book:  1,  11,  14,  24,  26,  36,  37,  53,  73. 

2.  Characteristics  of  Governors  (C-curves).  —  In  the  fur- 
ther treatment  of  the  properties  of  governors  as  speed  coun- 
ters it  is  advisable  to  deal  separately  with  spindle  governors 
and  with  shaft  governors.  The  latter  have  numerous  moments 
impressed  upon  them,  and  it  becomes  necessary  to  express  the 
equation  of  equilibrium  in  moments.  In  the  spindle  type  of 
governor  it  is  possible  and  advisable  to  deal  with  forces.  The 
treatment  of  the  spindle  type  is  therefore  simpler  and  will 
be  taken  up  in  the  following  paragraphs.  For  the  shaft  governor 
see  Chapter  VI. 

The  characteristic  properties  of  a  governor  as  a  speed 
counter  can  be  expressed  and  plotted  in  various  ways;  for 
instance,  we  may  plot  : 

(1)  equilibrium  speed  against  position  of  collar, 

(2)  equilibrium  speed  squared  against  position  of  collar, 

(3)  equilibrium  speed  against  radial  displacement  of  cen- 
trifugal weight, 

(4)  equilibrium  speed  squared  against  radial  displacement 
of  centrifugal  weight, 

(5)  centrifugal  force  against  radial  displacement  of  centrif- 
ugal weight. 


26      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

At  first  thought,  method  1  appears  to  be  the  most  con- 
venient and  to  offer  the  final  criterion.  Yet,  closer  study 
reveals  the  fact  that  method  1  shows  nothing  but  the  final 
result,  whereas  method  5  shows  most  of  the  hidden  mechanics 
of  the  governor. 

This  latter  method  was,  as  far  as  the  author  knows,  first 
used  by  Mr.  W.  Hartnell l  and  was  later  very  much  developed 
by  Mr.  M.  Tolle.2  The  Hartnell-Tolle  method  will  be  used  in 
this  and  the  following  paragraphs.  The  mass  of  the  links  will 
at  first  be  neglected. 

In  the  present  discussion  C  represents  that  radial,  out- 
wardly directed  force  which  balances  (directly,  or  by  means 
of  a  linkage)  all  other  forces  acting  in  the  governor,  such  as 

W  =  weight  of  centrifugal  masses 

Q   =  weight  of  counterpoise,  see  Fig.  16 

Si,  S2,  etc.  =  forces  exerted  by  springs 

F  =  equivalent  friction  forces,  see  paragraph  4  of  Chapter  II. 

The  line  of  action  of  C  passes  through  the  mass  center  of 
each  centrifugal  weight. 

In  order  to  develop  the  properties  of  characteristics  logically, 
we  start  with  a  simple  case,  namely  with  a  modified  type  of 
Watt  governor  (see  Fig.  16).  In  this  type  the  two  principal 
centripetal  forces  are  due  to  the  weights  W  and  Q.  It  is  ad- 
visable to  let  W  represent  the  weight  of  all  centrifugal  masses, 
because  Q  can  then  represent  the  weight  of  the  whole  counter- 
poise. Since  the  horizontal  force  C  balances  the  vertical  forces 
W  and  Q,  it  may  be  considered  as  consisting  of  two  components, 
Cw  and  Cq.  Cw  may  be  found  from  W  by  forming  moments 

about  fulcrum  (13),  so  that  Cw  =  W~.      Cq    can    likewise    be 

^i 

found  by  the  moment  method  ; 3  but  any  method  of  mechanics, 
including  graphic  statics,  may  be  employed.     After  the  forces 

1  Proceedings  of  British  Institute  of  Mechanical  Engineers,  1882. 

2  Zeitschrift  des  Vereins  Deutscher  Ingeriieure,  1895. 

3  The  lever  arm  of  Q  about  (13)  is  (13)-(14),  which  will  be  seen  from  the 
resolution  of  Q  into  a  horizontal  and  an  inclined  force.    Shift  the  latter  in  its  own 
direction  to  point  (14),  and  resolve  it  into  a  vertical  and  a  horizontal  force.    All 
horizontal  forces  cancel,  because  there  is  an  equal  and  opposite  force  on  the  other 
side  of  the  governor.    The  vertical  component  equals  Q. 


THE   GOVERNOR  AS  A   MEASURING   INSTRUMENT 


27 


Cw  and  C  q  have  been  found,  they  are  laid  off  directly  under 
the  center  (12)  of  weight  W  from  a  horizontal  base  line  (1) 
(15),  Fig.  16.  Thus  (15)  (10)  represents  Cw  to  some  scale, 
(15)  (7)  represents  Cq  to  the  same  scale,  and  (15)  (4)  represents 


FIG.  16 


C  =  Cw+Cq.  By  repetition  of  this  process  for  several  positions 
of  the  governor,  the  curves  (8)  (10)  (9),  (5)  (7)  (6)  and  (2)  (4)  (3) 
are  obtained. 

It  should  be  noted  that  in  the  construction  of  these  charac- 


28      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

teristic  curves  the  governor  has  been  treated  solely  as  a  mecha- 
nism and  not  as  a  speed  counter.  The  mechanism  in  this  case 
consists  of  a  slider  crank  with  fulcrum  (13)  and  slide  (11). 
The  location  of  the  governor  spindle  has  not  entered  the 
calculation.  Consequently,  the  shape  of  the  characteristic 
curves  of  a  weighted  governor  does  not  depend  upon  the 
location  of  the  governor  spindle  with  regard  to  the  mecha- 
nism (13)  (12)  (11).  Qn  the  other  hand,  we  certainly  must 
consider  the  location  of  the  characteristic  curve  relative  to 
the  spindle  if  we  wish  to  investigate  the  physical  properties 
which  it  represents.  To  that  end  we  must  replace  the 
auxiliary  horizontal  force  C  by  its  true  function  of  centrifugal 
force  of  the  revolving  masses.  Then 

C  =  mru1 (1) 

where 

m  =  mass  of  the  revolving  centrifugal  weights  ;  m  =  W/g 
r   =  radius  from  axis  of  rotation  to  mass  center  of  W.    The 
shape  of  the  centrifugal  weights  is  for  the  present 
limited  to  bodies  of  circular  section.    For  other  shapes 
see  paragraph  4  of  present  chapter. 

Ti 

u  =3.14  —  =  that  angular  velocity  at  which  equilibrium 
30 

exists  between  centrifugal  and  centripetal  forces. 
n  =  revolutions  of  governor  per  minute 

From  (1)  follows  u1  = .    In  order  to  be  able  to  tell  at  a 

r 

glance  the  value  of  u  for  different  positions  of  the  governor,  we 
introduce  the  following  trigonometric  relation  :  Calling  "i"  the 
angle  (4)(1)(15)  of  Fig.  16,  we  have  tan  i  =  C/r'=  mu2,  from 
equation  (1);  but,  since  m  is  constant,  tan  i  is  proportional 
to  u2,  or  u  is  proportional  to  -\/tan  i.  Hence  u  grows,  as  long 
as  i  grows;  it  falls,  whenever  i  decreases. 

Observation  of  the  angle  i  in  Fig.  16  teaches  that,  in  the 
type  of  governor  there  represented,  the  speed  grows,  as  the 
weights  move  outward.  The  question  is:  Must  this  be  so,  or 
would  it  be  just  as  good  to  have  the  speed  drop,  as  the  weights 
move  outward?  In  order  to  decide  this  question  refer  to 
Fig.  17,  in  which  (2)  (4)  (3)  is  a  governor  characteristic  with 


THE  GOVERNOR  AS  A  MEASURING  INSTRUMENT 


29 


rising  speed.  Imagine  that  the  governor  weights  are  displaced 
the  small  distance  dr  from  position  of  equilibrium  (4),  while 
the  speed  remains  constant.  The  centrifugal  force  grows 
from  (4)  (7)  to  (5)  (5),  but  the  centripetal  force  grows  at  the 
same  time  to  (£)(£),  so  that  a  centripetal  force  (6)  (5)  results 
which  urges  the  governor  back  to  its  position  of  equilibrium. 
The  governor  is  stable. 

If,  on  the  other  hand,  the  characteristic  had  followed  the 
line  (4)  (9),  the  displacement  dr  (at  constant  speed)  would 
have  produced  an  excess  centrifugal  force  (5)  (9)  which  would 


0 


•*-dr- 


FIG.  17 


urge  the  governor  still  farther  away  from  its  position  of  equi- 
librium. The  governor  would  be  unstable. 

The  rise  and  fall  of  the  angle  "i"  of  the  characteristic  in 
relation  to  the  radius  r  is  thus  a  certain  criterion  for  the  stability 
of  a  governor. 

A  quantitative  measure  of  the  stability  is  furnished  by  the 
well-known  expression  of  mechanics:  " Restoring  force  at  unit 
displacement."  Strictly  speaking,  this  expression  is  correct 
only,  if  the  restoring  force  is  proportional  to  the  displacement. 
In  the  absence  of  such  proportionality  we  must  use  the  ratio: 
restoring  force  at  a  given  small  displacement,  divided  by  that 
same  small  displacement.  In  the  case  of  a  centrifugal  governor, 

d(CP-C,) 


the  value  of  this  ratio  is  z  = 


dr 


where     Cp  =  centrip- 


GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

etal  force  and  C/  =  centrifugal  force.  For  the  interpretation 
of  this  equation  it  should  be  remembered  that  the  present 
investigation  considers  only  the  governor  by  itself,  running  on 
a  test  block,  so  that  pushing  the  governor  up  and  down,  away 
from  its  position  of  equilibrium,  does  not  alter  the  speed  at 
which  it  runs,  and  the  latter  remains  constant.  For  the  dis- 
placement dr,  Fig.  17,  (0)  (5)  is  the  restoring  force  d(Cp  -  Cf) 
which,  as  can  be  seen  from  the  illustration,  equals  the  differ- 
ential (with  regard  to  speed)  of  the  centrifugal  force  for  r  =  con- 
stant. But  dC  (for  r  =  constant)  equals  2  m  r  u  du.  Hence 

(6)  (5)       2mrudu 

the  stability  =  v  V  ;  =  -  -  =  z 

dr  dr 

du  du 

so  that  z=2mru*-2-  =  2C^- (2) 

dr  dr 

The  stability  of  a  governor,  when  running  on  a  test  block 
"by  itself "  and  not  governing  a  prime  mover,  is  proportional 

du 

to  the  total  centrifugal  force  and  to  the  value  — -       By    pass- 

dr 

ing  from  differentials  to  finite  differences  we  obtain 


du 


uu  -  ud 


u    =  approx.  \  (uu  +  ud)  p 

dr  TO  -  Ti 


2  Cp 
and  the  stability  z  =        —  —  .       An  elementary  derivation  of 

To  -   Ti 

this  equation  is  given  in  the  appendix.  This  latter  value  is 
an  approximation  only,  but  is  substantially  correct  for  straight- 
line  characteristics.  If  a  characteristic  is  curved,  the  value 
du 

-  must  be  used,  but  since  this  derivative  is  not  easily  con- 
dr 

structed  in  the  diagram,  it  is  advisable  to  fall  back  on  the 
trigonometric  function  given  on  page  28.  To  this  end  we  form 
the  complete  differential  of  C  and  obtain 


THE  GOVERNOR  AS  A   MEASURING   INSTRUMENT 

„  du      C  dr 


31 


dC  = 


u 


or 


u 


The  left-hand  member  of  this  equation,  if  divided  by  rfr,  equals 
the  stability  z,  hence 


z  = 


(3) 


But  dC/dr  =  tan  k,  and  C/r  =  tan  i  (see  Fig.  16). 

The  stability  of  a  governor  can,  therefore,  be  very  simply 
expressed  as  the  difference  of  the  tangents  of  two  angles.    Re- 


FIG.  18a 


FIG.  186 


ferring  again  to  the  same  illustration  we  note  that  the  angle  k 
is  formed  by  the  tangent  to  the  characteristic  at  that  point 
(4),  where  the  stability  is  to  be  determined,  and  that  the 
angle  i  is  formed  by  the  vector  drawn  from  the  origin  (1)  to 
the  point  (4)  on  the  characteristic.  From  the  fact  that  the 
stability  depends  upon  the  difference  between  the  tangents  of 
the  angles  k  and  i,  it  is  evident  that  the  governor  is  stable, 
whenever  the  point  of  intersection  (16)  lies  to  the  right  of  point 


32       GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

(1),  and  that  the  governor  is  unstable,  if  the  point  (16)  lies 
to  the  left  of  (1).  " Right"  and  "left"  must,  of  course,  be 
reversed  if  the  characteristic  is  drawn  to  the  left  of  the  spindle, 
instead  of  to  the  right  as  in  Fig.  16. 

From  this  influence  of  the  intersection  point  (for  instance: 
point  (16),  for  point  (4)  of  characteristic)  follows  the  important 
conclusion  that  any  weighted  governor  may  be  made  more 
sensitive,  or  less  stable,  by  moving  its  mechanism  closer  to  the 
axis  of  rotation.  The  shifting  of  the  relative  positions  of 
mechanism  and  of  axis  of  rotation  is  illustrated  in  Figs.  18a 
and  186.  In  both  cases  the  governor  mechanism  and  the  shape 
of  the  characteristic  are  identical,  but  the  stability  in  Fig.  18a 
is  considerably  greater  than  that  in  Fig.  186. 

It  is,  therefore,  possible  to  design  weight-loaded  governors 
(which  are  based  on  a  given  mechanism)  to  have  any  desired 

stability  by  simply  varying 
^"  the  location  of  the  mecha- 
nism relative  to  the  spindle. 
It  will  be  shown  later  on 
that  spring-loaded  governors 
can,  with  equal  or  even 
greater  facility,  be  designed 
for  any  desired  stability. 
However,  the  question  of 


©  .. 

what  stability  gives  the  best 

FIG.  19  .    ,.  ,  ,       ,      .  ,     , 

regulation  cannot  be  decided 

by  any  study  of  the  governor  alone;  it  requires  the  study  of  the 
interaction  of  governor  and  prime  mover.     See  Chapter  IX. 

Knowledge  of  the  properties  of  the  characteristic  clears 
up  the  widespread  confusion  between  the  terms  "stability" 
and  "static  fluctuation."  In  Fig.  19  three  characteristics, 
(2)  (4)  (3),  (2)  (5)  (3)  and  (2)  (6)  (3)  are  shown,  all  of  which 
have  the  same  static  fluctuation,  because  the  angles  iu  and  id 
are  the  same  for  all  three.  Tangents  drawn  to  the  curves  at 
different  points  show,  however,  that  the  characteristic  (2)  (5)  (3) 
is  unstable  near  point  (3) ,  whereas  the  characteristic  (2)  (6)  (3) 
is  unstable  near  point  (2).  From  this  difference  follows  that 
knowledge  of  the  static  fluctuation  alone  without  knowledge 


THE   GOVERNOR  AS  A   MEASURING  INSTRUMENT 


33 


of  the  shape  of  the  characteristic  is  not  sufficient  to  judge  the 
properties  of  a  governor. 

The  difference  between  the  two  terms  under  consideration 
will  be  further  emphasized  by  the  following  statement :  As 
far  as  the  governor  alone  is  concerned  —  apart  from  its  con- 
nection with  a  prime  mover  —  the  static  fluctuation  may  be 
decreased  without  decrease  of  stability,  by  utilizing  only  a 
small  part  of  the  radial  travel  of  the  weights.  Figure  16  shows 
that  confinement  of  the  weight  travel  between  the  vertical 
dash  and  dot  lines  reduces  the  static  fluctuation.  To  see  this 
more  clearly,  imagine  straight  lines  drawn  from  point  (1)  to 
intersections  (17)  and  (18)  of  the  vertical  dash  and  dot  lines 
and  the  characteristic.  The  angles  i  made  by  these  straight 
lines  with  the  axis  of  abscissae  vary  considerably  less  than  those 
made  by  the  straight  lines  drawn  from  •(!)  to  (2)  and  (3).  It 
will  be  remembered  that  angle  i  is,  to  a  certain  extent,  a  measure 
of  the  equilibrium  speed. 

While  limitation  of  radial  travel  has  been  frequently  em- 
ployed for  increasing  the  sensitiveness  of  governors,  and  while 
it  does  not  change  the 
stability  of  the  govern- 
or proper,  it  does 
decrease  the  stability 
of  regulation  of  a 
prime  mover  (see 
Chapter  IX).  It  also 
reduces  the  work 
capacity  of  the  govern- 
or and  necessitates 
the  use  of  a  stronger 
governor,  if  a  passive  resistance  is  to  be  overcome.  Finally,  it 
reduces  the  ability  of  the  governor  to  act  as  a  shock  absorber 
(see  Chapter  VIII). 

Engineers  who  wish  to  go  more  deeply  into  the  study  of 
characteristics  will  find  the  two  following  geometrical  relations 
of  interest:  The  first  of  them  expresses  the  static  fluctuation 
by  the  angles  i.  To  find  this  relation  we  transform  equation 
(1)  on  p.  23  in  the  following  manner  (see  Fig.  20): 


FIG.  20 


34      GOVERNORS  AND  THE  GOVERNING  OF   PRIME   MOVERS 


uu  -  ud         ,  (uu2  -  Ud2)         \mru      mrdj      tanu-  tanid 
~%(uu  +  ud)      f2(uu  +  Ud)2  Ca/mra  2  tan  ia 


In  these  equations  the  indices  u,  a,  and  d  mean  "up,"  "aver- 
age," and  "down." 

In  any  regulation  aiming  at  practically  constant  speed, 
ua  and  uu  differ  only  by  a  few  per  cent,  so  that  it  is  permissible 
to  write 

4-  Q  Y\     /i  4-  Q  Y"|     f\     , 

I  ill  I     v  u  I  ell  I.    v  d 

p  =  — = 

2  tan  iu 

The  second  relation  solves  the  problem  of  quickly  determin- 
ing the  equilibrium  speed  for  any  point  of  the  characteristic, 
if  the  equilibrium  speed  for  any  other  point  is  known.  Referring 
again  to  Fig.  20,  let  u^  point  (3)  of  the  characteristic  be  known, 
and  let  it  be  desired  to  find  u  at  point  (4).  Draw  ray  (1)(4) 
to  intersection  (6)  with  vertical  (3)  (8),  erect  semicircle  over 
(3)  (8),  draw  horizontal  through  (6)  to  intersection  (9)  with 
semicircle,  then  (8)  (9)  equals  u  of  point  (4)  to  the  same  scale 


to  which  (SX*)  equals  uu.       Proof:  —  =  L  =  but 

uu*       tani«       (3)  (8) 

by    construction    uu  =  (3)  (8),    so    that    it    cancels    out,    and 
u2  =  u  u  X  (0)(S)    remains,    which    means    that  u  is  the  mean 


proportional  of  (6)  (8)  and  (#)(<§).  The  construction  which 
is  given  above  makes  (8)  (9)  the  mean  proportional  of  these 
two  distances. 

References  to  Bibliography  at  end  of  book:    1,  11,  14,  26,  36,  36,  37,  52,  63, 
72,  73. 

3.  Constituent  Parts  of  the  Characteristic  Curve. — While 
the  analysis  of  the  preceding  paragraph  teaches  that  the 
principal  static  properties  of  a  governor  depend  upon  its  re- 
sultant characteristic,  more  detailed  study  proves  that  the 
individual  character  of  the  CQ  and  Cw  curves  is  of  equally  great 
importance. 


THE  GOVERNOR  AS  A  MEASURING  INSTRUMENT 


35 


In  order  to  obtain  sufficient  material  for  this  discussion, 
we  shall  investigate  the  characteristics  of  two  governors  quite 
different  from  the  Watt  type. 

(1)  Proell  type,  or  inverted  suspension  type,  Fig.  21.  In 
this  design  of  weight-loaded  governor  the  centrifugal  weight  is 


w 


Forces  are  those  of 
both  halves  of  governor 


FIG.  21 

not  carried  directly  by  the  pendulum  arm  (13)  (16),  but  forms 
part  of  the  connecting  rod  (11)  (16).  The  forces  CV  and  CQ 
are  found  by  forming  moments  about  the  instantaneous  center 
(14)-,  the  lever  arms  of  the  forces  have  been  marked  Lc,  Lw, 
and  LQ. 

In  the  illustration  the  forces  have  been  entered  to  scale*, 
and  the  CV  and  CQ  curves  have  been  drawn.     Study  of  these 


36     GOVERNORS   AND    THE    GOVERNING    OF    PRIME   MOVERS 


curves  shows  that  the  Cw  curve  is  slightly  unstable  in  its  inner 
part  (at  least  for  the  selected  location  of  the  governor  spindle) 
and  that  it  is  stable  in  its  outer  part.  The  CQ  curve  shows 
excess  stability.  By  variation  of  the  ratio  Q/W  the  stability 

of  the  governor  may  be 
varied.  In  the  illustra- 
tion, Q  is  so  much  greater 
than  W  that  the  governor 
has  considerable  stability, 
particularly  in  the  outer 
position. 

(2)  Hartnell  type, 
Fig.  22.  This  governor 
consists  of  two  (sometimes 
3  or  4)  centrifugal  weights 
TFwith  mass  centers  (12)} 

III    'Q  (17)1/^1 — ^vv*  Cs      ^e  weignts  are  carried  on 

J  I  L  ®  //  kell     cranks     with     fixed 

fulcrums     (18).       The 
principal  centripetal  force 
is  furnished   by  an  axial 
spring.     Again  CQ  and  Cw 
can  be  found  by  moments 
about   the   pivots,    which 
are  represented  by  points 
(13)    in   this   case.     Q   is 
variable  in  this  governor 
so  that  doubt  may  arise 
concerning   the   meaning 
FIG.  22  of  CQ.    For  reasons  which 

will    appear    later   it    is 

advisable  to  plot  CQ  for  a  constant  force  Q.  For  the  latter,  we 
assume  an  arbitrary  constant  unit  force  applied  at  point  (14). 
Both  the  Cw  curve  (8)  (10)  (9)  and  the  CQ  curve  (5)  (7)  (6) 
show  a  decidedly  negative  static  fluctuation  ;  note  that  tan  i 
drops.  To  render  the  governor  useful,  the  central  force  Q 
must  be  made  variable  to  such  an  extent  that  the  resulting  C 
curve  furnishes  a  small  positive  fluctuation.  Disregarding  for 


THE  GOVERNOR  AS  A  MEASURING  INSTRUMENT  37 

the  present  the  limitations  which  may  be  imposed  by  the 
space  available  for  the  spring,  we  can  determine  the  required 
spring  force  as  follows;  Draw  the  desired  characteristic 
(15)  (17)  (16),  and  the  CQ  curve  for  those  weights  which  move 
up  and  down  with  the  sleeve  (18).  These  weights  include  that 
of  the  sleeve,  of  roller  (14),  of  the  plate,  and  one  half  of 
the  spring.  Add  the  ordinates  of  this  CQ  curve  and  of  the 
Cw  curve.  Find  the  differences  between  this  combined  curve 
and  the  desired  final  C  curve.  These  differences  divided  by 
the  ordinates  of  that  CQ  curve  which  belong  to  Q  =  1  furnish 
the  spring  forces.  The  first  attempt  may  result  in  impossible 
spring  dimensions,  or  in  improper  utilization  of  the  available 
space,  but  it  will  show  in  which  direction  the  assumptions  of 
the  resulting  C  curve  must  be  altered. 

The  description  of  these  governors  and  of  the  construction 
of  the  characteristic  curves  is  rather  sketchy,  but  illustrations 
16,  21  and  22  contain  sufficient  information  for  studying  the 
individual  influence  of  the  Cw  and  CQ  curves. 

When  a  governor  governs  a  prime  mover,  it  is  subjected 
to  forces  acting  upon  its  sleeve,  that  is  to  say  forces  which 
either  add  to  or  subtract  from  Q.  Such  forces  are  caused  by 

(1)  Adjustment  of  equilibrium  speed. 

(2)  Resistance  to  motion  caused  by  friction  of  valve  gear. 

(3)  Unbalanced  weights  or  fluid  pressure. 

(4)  Integrated  effect  of  valve  gear  reaction. 

Speed  adjustment  is  usually  accomplished  by  the  addition 
or  subtraction  of  a  constant  force,  see  Chapter  V,  for  instance 
by  the  shifting  of  a  weight  along  a  lever  or  by  the  tightening 
of  a  helical  spring.  The  addition  of  a  constant  force  at  the 
sleeve  produces  a  proportionate  increase  or  reduction  of  the 
ordinates  of  the  CQ  curve.  If  the  CQ  curve  and  the  Cw  curve 
are  both  stable  and  of  the  same  character  as  the  combined 
curve,  such  as,  for  instance,  in  Fig.  16,  the  addition  or  sub- 
traction of  a  constant  force  does  not  affect  the  static  character 
of  the  governor.  But  if  the  CQ  curve  has  excess  stability  in 
order  to  make  up  for  insufficient  stability  of  the  Cw  curve,  see 
Fig.  21,  any  addition  to  Q  increases  the  stability,  and  a  reduc- 
tion of  Q  reduces  the  stability  of  the  governor.  If,  finally, 


38       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

the  CQ  curve  has  negative  stability  (which  is  the  case  in  most 
spring-loaded  governors,  such  as  in  22)  an  addition  to  Q  makes 
the  governor  less  stable,  and  if  carried  far  enough,  makes  it 
utterly  unfit  for  regulation.  This  effect  of  the  addition  of  a 
constant  force  is  always  the  same,  no  matter  whether  it  conies 
from  item  1,  2,  3  or  4  of  the  above  given  classification. 

The  forces  entering  the  governor  through  the  sleeve  are  a 
fruitful  source  of  annoyance  and  of  triangular  litigation  between 
the  builder  of  the  governor,  the  builder  of  the  prime  mover 
and  the  user  of  the  latter.  Thus,  the  excessive  clogging  of 
regulating  valves  with  tar  in  gas  engines,  the  excessive  and 
onesided  tightening  of  stuffing  box  glands  of  regulating  spindles 
in  engines  and  turbines  furnish  complaints  for  which  neither 
the  governor  builder  nor  the  builder  of  the  prime  mover  is 
responsible,  except  that,  perhaps,  the  latter  did  not  install  a 
large  enough  governor. 

If  these  forces  are  constant  throughout  the  working  range  of 
the  governor,  they  will  only  alter  the  equilibrium  speed,  but 
will  not  upset  stability  of  regulation,  provided  that  the  CQ 
and  Cw  curves  have  like  character  and  stability. 

As  a  rule,  the  forces  resulting  from  items  2,  3  and  4  of  the 
list  on  page  47  vary  with  the  position  of  the  governor  sleeve. 
In  gas  engines  there  may  be  (and  there  usually  is)  more  tar 
deposit  near  one  end  of  the  swing  of  the  regulating  valve  than 
there  is  near  the  other  end.  So-called  balanced  regulating 
valves  are  frequently  so  designed  that  they  appear  at  first 
glance  to  be  balanced,  but  are  really  not  so,  because  near  the 
closed  position  forces  arise  from  impact  or  jet  action  of  the 
fluid.  These  forces  are  transmitted  to  the  governor  and,  by 
their  action  at  one  end  of  the  travel  only,  often  seriously 
upset  regulation. 

For  the  purpose  of  this  book  it  will  suffice  to  study  the 
action  of  two  types  of  these  so-called  balanced  valves.  Fig.  23 
shows  a  double  beat  poppet  valve,  the  bottom  seat  of  which 
is  slightly  smaller  than  the  upper  one,  for  assembling  purposes. 
Each  valve  is  cup  shaped  for  purposes  of  strength  and  rigidity. 
When  the  valve  is  wide  open,  there  is  an  upward  thrust, 
because  there  is  then  maximum  flow,  and  because  the  concave 


THE   GOVERNOR  AS  A  MEASURING  INSTRUMENT 


39 


Steam 
Pressure 


Throttle 
Pressure 


FIG.  23 


side  offers  more  resistance  to  flow  than  the  convex  side  does. 
With  an  almost  closed  valve,  that  is  to  say  with  very  low  rate 
of  discharge,  there  is  a  downward  thrust.  In  this  position  of 
the  valve,  the  upstream  steam  pressure  is  much  greater  than 
the  downstream 
throttle  pressure,  and 
a  static  pressure 
effect  due  to  the  dif- 
ference of  areas  of 
upper  and  lower 
valve  is  felt. 

So-called  bal- 
anced butterfly 
valves  are  usually 
quite  unbalanced, 
because  the  "  noz- 
zles" in  which  pres- 
sure is  converted  into  velocity  have  very  dissimilar  shapes  on  the 
two  sides  of  the  valve.  The  lines  (Jf)(£)(3)  of  Fig.  24  are 
intended  to  show  respectively  equal  areas  of  flow  and  niveau 
surfaces  of  respectively  equal  pressure.  It  is  evident  that  the 
pressure  drop  takes  place  with  less  travel  at  the  bottom  of  the 

valve,  so  that  a  larger 
part  of  the  bottom 
wing  is  exposed  to  high 
pressure  than  there  is 
at  the  top.  Conse- 
quently a  force  results 
in  the  direction  of 
arrow  (4).  When  the 
valve  is  opened,  this  force  disappears. 

The  injurious  influence  which  these  unbalanced-in-certain- 
positions  valves  have  upon  satisfactory  regulation  has  caused 
many  engineers  to  keep  the  unbalanced  forces  away  from  the 
governor  by  interposing  a  relay,  see  Chapter  XIII.  But  if 
a  relay  is  not  used,  the  forces  in  question  should  be  made  as 
small  as  possible  by  the  builder  of  the  prime  mover;  besides, 
the  governor  designer  should  be  notified  of  the  extent  of  these 


FIG.  24 


40       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


forces,  so  that  he  may  provide  for  them  in  the  design  of  the 
governor.  In  doing  the  latter  he  will  again  make  use  of  the 
CQ  curve.  If  such  a  curve  be  drawn  for  Q  =  1,  the  ordinate 
belonging  to  any  given  position  of  the  governor  sleeve  can  be 
multiplied  by  the  force  reacting  upon  the  sleeve  in  the  position 
under  consideration.  Repetition  of  this  method  for  several 
positions  of  the  sleeve  furnishes  a  new  C  curve  for  the  forces 
entering  the  governor  from  without.  Combination  of  this 
curve  with  the  other  C  curves  must  result  in  a  curve  with  posi- 
tive static  fluctuation,  as  previously  explained,  if  correct  regu- 
lation is  desired. 

References  to  Bibliography  at  end  of  book:   11,  36,  53,  72,  73 

4.  Influence  of  Shape  of  Centrifugal  Weights  on  Character- 
istics.--The  subject  of  the  present  paragraph  is  not  of  vital 
consequence  for  any  centrifugal  governor  now  on  the  market; 
neither  is  it  likely  to  be  of  such  consequence.  It  might,  there- 
fore, be  passed  in  silence,  if  it  were  not  for  the  human  fail- 
ing of  reinventing  designs  which  were  relegated  to  the  scrap 

heap  long  ago.  And  "  Improving  CL 
governor"  by  changing  the  shape  of 
the  centrifugal  weights  is  a  popular 
subject  for  inventors. 

In  paragraphs  2  and  3  of  the  present 
chapter  the  theory  of  the  characteristic 
curves  of  governors  was  developed  for 
centrifugal  weights  of  spherical  or  other- 
wise  symmetrical  shape,  and  the  state- 
ment was  made  that  for  such  shapes  it 
was  permissible  to  concentrate  the  whole 
mass  of  the  weight  in  its  mass  center. 
The  correctness  of  this  statement  will  now  be  analyzed. 
In  Fig.  25  the  oval  shape  represents  a  centrifugal  weight 
with  mass  center    (0),   and  with  suspension  point    (1).     The 
moment  of  the  centrifugal  force  of  a  small  mass  dm  about  the 
suspension  point  is  dM  =  dm  u2(r  +  x)  (y  +  L) .     For  meaning 
of  r  and  L  see  illustration.    The  moment  of  the  whole  mass  is 
the  integral 


FIG.  25 


THE  GOVERNOR  AS  A  MEASURING  INSTRUMENT  41 

M  =  u2fdm(r  +  a;)  (y  +  L),  or 

M  =  u2  r  fdm  y  +  u2  r  L  fdm  +  u2  fdm  x  y  +  u2  L  fdm  x. 

By  definition  of  the  mass  center,  f  dm  y  =  0,  and  f  dm  x=Q. 
It  is  also  evident  that  fdm  =  m,  so  that  the  centrifugal  moment 
of  the  weight  is  reduced  to  M  =  u2  r  L  m  +  u2  f  dm  x  y. 

In  the  preceding  paragraphs  centrifugal  force  had  been 
given  as  m  r  u2  and  centrifugal  moment  as  u2  r  L  m.  Evidently, 
the  actual  moment  differs  by  the  amount  u2  f  dm  x  y,  and  the 
equivalent  centrifugal  force  which,  when  acting  at  the  mass 
center,  produces  the  correct  moment  is 

C  =  r  u2  (m  +  —fdm  xy\ (1) 

For  all  shapes  which  are  symmetrical  with  regard  to  two 
axes  at  right  angles  to  each  other,  fdm  x  y  =  0.  Such  shapes 
are  the  circle,  the  square,  the  octagon,  etc.  For  centrifugal 
weights  of  any  one  of  these  forms  the  assumption  that  the  mass 
may  be  concentrated  in  the  mass  center  is,  therefore,  correct. 
For  all  other  shapes  the  theories  of  paragraphs  2  and  3  must 
be  modified. 

To  carry  out  this  modification,  it  is  desirable  to  narrow 
down  somewhat  the  extent  of  the  investigation,  because  the 

value  of  the  correction  —:  f  dm  x  y  in  equation    (1)  cannot  be 

rL 

weighed  or  appreciated  in  its  general  form.  If  the  investigation 
is  limited  to  weights  whose  thickness  h  is  constant  at  right  angles 
to  the  plane  in  which  they  swing,  the  correction  can  be  put 
into  a  form  which  presents  a  fairly  clear  view  of  the  influence 
of  the  shape.  To  this  end  we  use  the  principal  axes  (3)  (4) 
and  (5)  (6)  of  the  plane  section  of  the  swinging  weight  as  a 
new  system  of  coordinates. 

Let  mf  =  mass  of  unit  volume  in  centrifugal  weight;  J8 
and  Ji  =  the  smallest  resp.  largest  moment  of  inertia  of  the 
plane  section  of  the  centrifugal  weights;  k  =  the  angle  between 
the  axis  of  rotation  and  the  axis  to  which  the  smallest  moment 
of  inertia  is  referred;  then  we  have 

fdm  x  y  =  \  m'  h  (  Jt  -  J  s)  sin  2  k (2) 


42      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

For  proof  of  this  equation  see  Appendix,  p.  214. 

From  equation  (2)  it  follows  that  the  difference  of  the  two 
principal  moments  of  inertia  and  the  angle  k  of  the  inclination 
of  the  axis  determine  the  extent  of  the  correction.  For  k  =  0°, 
and  for  k  =  90°,  the  value  of  the  correction  is  zero.  The  same 
is  true  for  any  value  of  k,  if  Js  =  Jt,  which  bears  out  the  state- 
ments made  above  concerning  symmetrical  shapes.  The  dif- 
ference between  J  '  a  and  Ji  is  the  greater,  for  a  given  area  of 
section,  the  more  oblong  the  shape  of  the  weight. 

Let  Cp  L  =  M  p  be  the  centripetal  moment  —  caused  by 
spring  forces,  weights,  etc.  —  which  is  to  be  balanced  by  the 
centrifugal  moment  Mc,  and  let  Cp  be  the  equivalent  centrip- 
etal force  referred  to  the  center  of  each  centrifugal  mass  ; 
then 

CpL  =  mru2L+%m'hu2(Ji-  Js)  sin  2  k, 

from  which 

,  __  Cp  __    CP  1  _ 

1  =  mr^  .  m'M/r-Js)sin2A;(3) 

mr  +  —mfh(Ji-Js)sm2k 


s 

It  will  be  remembered  that,   for  symmetrical  centrifugal 
weights,  the  static  properties  of  a  governor  were  found  from 

C        tan  i 

its  characteristic  by  means  of  the  equation  v?  =  —  =  -  - 

mr         m 

Equation    (3)   teaches  that  this  simple  relation   does   not 
hold  for  governors  with  oblong  weights.     However,  a  charac- 

C" 

teristic  may  be  so  drawn  with  ordinates  C'  that  u2  =  —  •  ,     pro- 

mr 

vided  that  we  make 


C 


m'h(Jl-Js)sm2k 
2Lmr 


Evidently,  the  relations  between  sin  2  k,  L  and  r  in  conjunc- 
tion with  the  value  of  (Jt  —  Js)  determine  the  difference  between 
Cp  and  C'.  In  general,  the  difference  is  greatest  for  k  =  45°. 

C 

Whereas  for  symmetrical  shapes  of  weights  tan  i  =  -  •  =  con- 

mr 


THE   GOVERNOR  AS  A  MEASURING  INSTRUMENT 


43 


stant,  that  is  to  say,  a  straight  line  characteristic  passing 
through  the  origin,  means  an  isochronous  governor,  it  does  not 
convey  the  same  meaning  for  a  governor  with  oblong  weights. 
On  the  contrary,  the  characteristic  for  an  isochronous  governor 
with  oblong  weights  is  curved,  the  magnitude  of  the  curvature 
depending  principally  upon  (Jl  —  Js). 

Equations  (3)  and  (4)  express  the  conditions  quite  clearly 
from  a  mathematical  standpoint.  A  less  comprehensive,  but 
ver>  much  simpler  explanation  of  the 
effect  of  the  shape  of  the  centrifugal 
weights  upon  the  speed  and  upon  the 
shape  of  the  characteristic  can  be 
gained  by  studying  the  effect  of  split- 
ting a  concentrated  centrifugal  mass 
into  two  concentrated  masses  some 
distance  apart  and  joined  by  a  mass- 
less  rod. 

In  Fig.  26  the  centrifugal  moment 
of  a  mass  ra  at  point  (1)  is  M  = 
ra  u^  4  s2.  If  the  mass  ra  is  split  into 
two  masses  |  ra,  located  at  points  (2) 
and  (3}j  the  moment  appears  in  the  form  M  =  |  ra  u2z(l2  +  32)  s2 
=  ra  u^  5  s2.  If,  finally,  the  masses  \  ra  are  located  at  points 
(4)  and  (5),  the  moment  becomes  M  =  J  ra  M32(02  +  42)  s2  = 
ra  Uz  8  s2.  The  moment  M  remains  the  same  in  all  three  cases, 
because  the  centripetal  (in  this  case  gravity)  moment  is  the 
same.  The  speeds  are  found  from  the  foregoing  equations  by 
solving  for  u. 

^~  i/l     i/~^~  */l    »/^" 

u>  =  V-  V- 


FIG.  26 


m  s4 


8 


The  oblong  shape  of  weight  evidently  lowers  the  equilibrium 
speed,  if  the  weight  is  arranged  as  in  Fig.  26. 

The  reverse  action  takes  place  if  the  long  axis  of  the  mass 
is  placed  as  in  Fig.  27.  The  moment  equation  for  the  mass  at 
point  (1)  is  M  =  m  Ui2  4  s2.  For  two  masses  \  ra  at  points  (2) 

7TL 

and   (3}  it  is  M  =  —  u<?  (3  +  3)  s2,  and  for  two  masses  \  ra  at 


44       GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


points  (4)  and  (5)  it  is  M  ==  ^32(0  +  0)  s2,  whence  the  speeds 


and 


ws 


ras 


0 


?s 


In  the  arrangement  of  Fig.   27   the  oblong  shape  of  the 
weight  raises  the  equilibrium  speed. 

The  influence  of  the  shape  of  oblong  weights  may  be  utilized 
by  skillful  designers  for  obtaining  weight-loaded  governors  of 

small  static  fluctuation  and  constant 
stability.  Governors  based  upon  this 
principle  were  designed  several 
decades  ago.  The  best  known  ex- 
ample is  the  cosine  governor.  To- 
day, these  governors  can  only  be 
found  in  textbooks  and  mathematical 
treatises.  For  a  given  strength, 
oblong  swinging  weights  increase  the 
mass  of  a  governor,  and  reduce  its 
promptness  (see  Chapter  IV).  But 
governors  whose  mass  is  large  com- 
pared to  their  strength  produce  great  speed  fluctuations  when- 
ever the  load  changes.  This  fact,  the  correctness  of  which  will 
be  proved  in  paragraph  2  of  Chapter  IX,  by  the  introduction 
of  the  traversing  time  T  g,  has  practically  eliminated  the  governor 
with  oblong  swinging  weights. 

In  shaft  governors  the  shape  of  the  weight  has  no  influence 
on  the  speed  or  on  the  characteristic  (see  Chapter  VI). 

References  to  Bibliography  at  end  of  book:  36,  73. 


27 


CHAPTER  IV 

PROMPTNESS  AND  TRAVERSING  TIME 

IN  the  chapter  treating  of  the  relation  between  governor 
and  prime  mover,  proof  will  be  furnished  that  closeness  of  regu- 
lation requires  quick  motions  of  the  governor  after  a  disturbance 
of  equilibrium. 

The  property  of  a  governor  to  move  quickly  to  a  new 
position  has  been  termed  " promptness"  by  French  engineers. 
Unfortunately,  promptness,  like  sensitiveness,  is  hard  to 
define. 

On  the  other  hand  there  exists  a  convenient  term  which  is 
closely  related  to  promptness,  can  be  correctly  defined,  and 
appears  in  all  dynamic  calculations  on  governors;  this  term 
is  the  "  traversing  time."  Its  meaning  is  exhibited  most 
clearly  by  the  following  illustration :  Let  the  centrifugal  weights 
of  a  non-rotating,  frictionless  governor  be  moved  to  their 
extreme  outward  position  and  then  be  suddenly  released. 
Starting  with  zero  velocity,  they  traverse  the  path  to  their 
extreme  inward  position  with  increasing  speed,  under  the  influ- 
ence of  the  centripetal  forces  or  moments,  in  the  "  traversing 
time."  From  mechanics  it  is  known  that  to  make  this 
time  small,  we  must  make  the  acting  forces  great,  the  inertia 
of  the  moving  masses  small  and  the  distance-to-be-traversed 
short. 

If  either  the  centripetal  moment  Mp  (about  any  one  axis), 
or  the  moment  of  inertia  of  the  governor  parts  (about  the  same 
axis)  vary  widely,  determining  the  traversing  time  requires 
either  a  graphical  integration,  or  else  a  dividing-up  of  the 
total  travel  into  sections  over  each  of  which  the  variable  quan- 
tities may  be  considered  as  constant.  In  all  practical  work, 
however,  it  is  customary  and  permissible  to  replace  these 
variables  by  their  mean  values.  With  this  simplification  the 

45 


46      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

traversing  time  can  easily  be  calculated    from    the    equation 
which  holds  for  constant  acceleration,  namely 

T    - 

•L  a  ~ 

In  this  equation 
T g   =  traversing  time 
J     =  moment  of  inertia  of  governor  parts 
Mp  =  centripetal  moment 
i      =  total  angle  through  which  the  gover- 


ref erred  to  the  same 
axis  of  rotation 


nor  parts  swing 

mf  =  equivalent  mass  of  governor  parts  referred  to  radial  travel 
ma  =  equivalent  mass  of  governor  parts  referred  to  axial  travel 
b,  s,  =  total  radial,  resp.  axial  travel 
C     =  centripetal  force 
P     =  strength  of  governor. 

Smallness  of  the  traversing  time  as  a  measure  of  prompt- 
ness might  be  objected  to,  because  under  actual  working 
conditions  the  moment  Mp  resp.  the  forces  C  or  P  are  not 
available  in  full  strength.  Neither  do  the  governor  parts 
traverse  their  whole  range  of  travel  under  ordinary  changes 
of  load.  Any  such  objection  overlooks  the  fact  that  both  the 
available  fraction  of  the  force  or  moment  and  the  fraction  of 
the  travel  to  be  traversed  are  proportional  to  the  change  of 
load,  so  that  these  fractions  cancel  in  the  equation  for  the 
traversing  time.  Hence  the  time  T  g  is  a  true  measure  for  the 
slowness  of  the  frictionless  governor,  and  l/T g  is  a  measure  for 
the  quickness  or  promptness  of  the  governor. 

In  a  purely  centrifugal  governor  the  time  T  g  can  be  made 
small  by  increase  of  C  and  by  reduction  of  mr;  fulfillment  of 
both  of  these  conditions  excludes  weight-loaded  governors  and 
necessitates  spring-loaded  governors.  In  the  latter  type, 
increase  of  C  and  reduction  of  mr  are  accomplished  by  great 
angular  velocity  and  by  large  orbit  of  centrifugal  masses. 
Finally,  smallness  of  path  (angular  path  i,  or  linear  path  s,  b) 
increases  the  promptness.  Limitations  are  furnished  by  cost. 
Evidently  larger  and  larger  orbits  and  higher  angular  velocities 
cause  mechanical  difficulties  and  increased  cost. 


PROMPTNESS  AND   TRAVERSING  TIME 


47 


The  reduction  of  mass  which  is  so  desirable  for  the  sake  of 
promptness  is  very  undesirable,  if  the  governor  is  subjected  to 
displacing  forces  or  reactions  caused  by  the  valve  gear  (see 
Chapter  VIII).  If  a  massive  and  yet  prompt  governor  is 
desired,  it  must  be  made  very  powerful,  or  else  tangential 
inertia  must  be  utilized.  Inertia  masses  increase  J,  mr  or  ma 
in  equation  (1)  and  are,  therefore,  injurious  to  promptness,  as 
expressed  by  that  equation.  On  the  other  hand,  tangential 


FIG.  28 

inertia  furnishes  a  regulating  force  whose  value,  as  was  shown 
in  paragraph  2  of  Chapter  II,  grows  with  the  suddenness  of 
the  change  of  load.  To  what  extent  this  feature  increases  the 
promptness  cannot  be  treated  without  knowledge  of  the  dy- 
namics of  regulation.  See  paragraph  3  of  Chapter  IX. 

The  following  brief  calculation  of  the  traversing  time  of 
a  spring-loaded  governor  will  illustrate  the  use  of  equation  (1): 


48      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


In  the   governor   shown  in   Fig.   28,   the  equivalent  mass 

3.25 
2.81 


157.5      JX  13      |  X  16.5        40        /3.25V 
:~  ~~       ~~    h          X  V2/  = 


(1)  (2)  (3)  (4) 

In  this  equation  (1)  is  the  mass  of  the  centrifugal  weights, 

(2)  is  part  of  the  mass  of  the  bell  cranks, 

(3)  is  part  of  the  mass  of  the  springs, 

(4)  is  the  equivalent  mass  of  the  weight  of  the  sleeve  and 

/3.25V 
of  other  parts  moving  with  it.     The  factor  (-    -J  reduces  that 

\-Z.oI' 

mass  to  the  radial  travel  of  the  weights. 

Radial  travel  b  =  2.81" 

Mean  centripetal  force  C  =  1200  pounds. 

With  these  values  —  which  were  found  by  measurement  of 
a  governor  in  the  Mechanical  Engineering  Laboratory  of  the 
Carnegie  Institute  of  Technology  —  we  obtain  the  traversing 
time 


=  J2  X  6.95  X  2.81 


"1200^12" 

For  the  greatest  accuracy  it  would  be  necessary  to  take 
cognizance  of  the  fact  that  the  weights  move  on  an  arc,  and 
that,  for  this  reason,  the  equivalent  mass  should  be  multiplied 
by  a  factor  greater  than  one;  but  this  factor  is  in  the  present 
case  so  near  one  that  it  is  permissible  to  neglect  it. 

The  traversing  time  of  a  weight-loaded  governor  is,  of 
course,  much  greater,  unless  exceedingly  short  radial  travels 
of  the  centrifugal  masses  are  used. 

In  the  governor  shown  in  Fig.  56  the  average  strength  P 
is  500  pounds.  The  axial  travel  of  the  collar  is  s  =  3.25  inches. 
The  equivalent  mass  is  that  of  all  the  parts  moving  with  the 
collar  plus  that  of  the  balls,  the  latter  multiplied  by  the  ratio 

/travel   of  ballsy  542 

—  -  —  -  -  r—  J  .     The  total  equivalent  mass  is  —  —  —  —    in 
Vtravel  of  collar/  12  X  32.2 

inch,  pound,  second  units.     Hence,  the  traversing  time  is 


Reference  to  Bibliography  at  end  of  book:  36. 


CHAPTER   V 

ADJUSTMENT  OF  EQUILIBRIUM   SPEED 

(1)  Slight  errors  in  calculation  or  workmanship,  and  varia- 
tion in  the  material  of  spring  steel  prevent  governors  from 
running  at  the  intended  speed.     Unforeseen  reaction  from  the 
valve  gear  has  the  same  result. 

Such  conditions  call  for  a  single  adjustment  or  a  short 
series  of  adjustments. 

(2)  For  synchronizing  purposes  or  for  adjustment  of  voltage 
the  speed  of  engines  or  turbines  must  be  varied  up  to  3  or  4  % 
either   way   from  mean.      Regulation   must   be   equally   exact 
with  any  one  of  the  adjusted  mean  speeds. 

(3)  For    the    regulation    of   pumping    machinery,    whether 
of  the  displacement  or  of  the  velocity  type,  the  equilibrium 
speed    must    be    adjusted    within     wide    limits;     the    ratio 

highest  equil:brium  speed 

....    .  — r  occasionally  reaches  values  of  3  or  4. 

lowest  equilibrium  speed 

Fortunately  the  requirements  for  exactness  of  regulation  are 
not  so  strict  in  this  case. 

The  adjustment  or  adjustments  (1)  can  be  made  while  the 
prime  mover  and  the  governor  stand  still,  whereas  the  adjust- 
ments (2)  and  (3)  must  be  made  with  the  governor  in  motion. 

For  the  adjustments  (1)  a  number  of  methods  exist,  such 
as  change  of  mass  of  centrifugal  weights  (drilling  of  holes, 
filling  with  lead),  change  of  spring  tension,  variation  of  spring 
scale  (grinding  off  the  outer-diameter  fiber  of  helical  springs, 
cutting  off  end  coils,  etc.),  change  of  lever  arm  of  spring,  and 
others. 

For  the  adjustments  under  (2)  and  (3)  the  following  means 
are  available  : 

(1)  Change  of  speed  ratio  between  prime  mover  and  governor 
(equilibrium  speed  of  governor  remains  constant)  attained  by 

(a)  change  gears, 

(b)  friction  discs  or  conical  pulleys; 

49 


50       GOVERNORS  AND   THE   GOVERNING  OF  PRIME   MOVERS 


either  of  these  subdivisions  can  be  constructed  in  different 
forms  mechanically. 

(2)  Change  of  equilibrium  speed  by  variation  of  axial  force 
Q,  acting  on  collar.  Shaft  governors  need  no  collar  while  gov- 
erning prime  movers  (see  Chapter  VI),  but  an  element,  equiva- 
lent to  a  collar,  is  occasionally  provided  solely  for  the  purpose 
of  speed  adjustment. 

Variation  of  Q  may  be  ob- 
tained by 

(a)  addition  or  subtrac- 
tion of  mass  (water,  etc.)  or  of 
fluid  pressure 

From  Shaft  of 
Prime  Mover 


E  ^fl—r- 1— fl*  5  To  Governor 


FIG.  29 


(b)  variation  of  the  lever  arm  of  a  force 

(c)  variation  of  spring  tension 

(3)  Variation  of  governor  mechanism,  for  instance,  displace- 
ment of  movable  fulcrum  (for  illustration  see  Fig.  39). 

(4)  Change  of  relative  position  between  power  controlling 
mechanism  and  position  of  governor  (for  illustration  see  Fig.  40) . 

Method  (1)  makes  possible  a  wide  range  of  speed  adjust- 
ment. Change  gears,  one  design  of  which  is  diagrammatically 
shown  in  Fig  29,  act  in  steps  and  must  be  used  in  connection 
with  other  adjusting  means  to  make  gradual  adjustment  over 
the  whole  range  possible.  Even  then  there  is  a  jump  whenever 


ADJUSTMENT  OF  EQUILIBRIUM   SPEED 


51 


the  change  in  the  gears  is  made,  so  that  change  gears  have  their 
limitations. 

Frictional  devices  (for  diagrammatic  illustration  see  Fig.  30) 
are  very  satisfactory,  provided  that  they  are  large  enough 
to  prevent  serious  slipping.  The 
latter  is  caused  particularly  by 
the  frictional  resistance  of  the 
governor  and  by  cyclical  speed 
fluctuations. 

Frictional  devices  have  come 
into  disrepute  for  large  prime 
movers,  because  designers  have 
hesitated  to  use  the  unsightly 
large  friction  discs  which  are 
necessary  for  success  and  have 
put  "more  decent  looking " 
smaller  sizes  on  the  engines.  The 
result  in  such  cases  invariably  is 
slippage,  wear,  unsatisfactory 
regulation  and  thoughtless  con- 
demnation of  the  entire  principle. 

Detail  description  of  these 
devices  and  calculation  of  neces- 
sary sizes  is  prohibitive  on 
account  of  the  endless  variety  of 
possible  designs  and  arrange- 
ments. 

Means  No.  (2),  that  is  to  say 
variation  of  axial  force  Q,  is  by 
far  the  most  common.  In  para- 
gaph  3  of  Chapter  III  the  use  of 

the  C  curves  for  an  investigation  of  the  stability  of  the  governor 
with  varying  values  of  Q  was  indicated.  It  will  now  be  further 
illustrated  by  means  of  an  example  which  is  based  on  the  type 
shown  in  Fig.  22;  this  type  has  been  widely  adopted  in  steam 
turbine  practice. 

The  governor  is  shown  in  Fig.  31.    For  the  numerical  calcu- 
lation the  following  values  were  used: 


FIG.  31 


52      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


Weight  of  both  centrifugal  masses  W  =  15  pounds 
Weight   of   axially  moving  parts    (including   f   weight   of 
spring)  =  45  pounds 

Travel  of  collar  s  =  2  inches 

Initial  tension  of  spring  =150  pounds  and 
150  +  85  pounds 

Scale  of  spring  =  140  pounds  per  inch. 

The  characteristics  CQ  are  easily  drawn  if 
it  is  remembered  that  the  direction  of  Q,  CQ 
and  of  their  resultant  are  given  (see  Fig.  32) 
because  the  latter  must  pass  through  the  fixed 
fulcrum.  The  detail  construction  of  the 
characteristics  is  given  in  the  Appendix, 
p.  215.  The  characteristics 
proper  are  shown  in  Fig.  31. 

c 


From  u 


it  follows 


FIG.  32 


m  r 


for  position  (3)  n\  =  268 
r.p.m.  (initial  tension  =  130  lb.),  and  n2  = 
300  r.p.m.  (initial  tension  =  215  lb.)  so  that 
the  tightening  of  the  spring  has  produced  12  % 
increase  of  speed.  The  static  fluctuation  (see 
page  24)  is  found  for  the  small  initial  tension 


from  pi  = 


(33)  (3  4) 


2  X  (35)  (36) 
in  the  same  way  we  find 


which  equals  15.1%; 

(30) (31) 


FIG.  33 


2  X  (32) (36) 

which  equals  5.8%.  Evidently  the  static 
fluctuation  is  considerably  reduced  by  the 
tightening  of  the  spring.  The  stability  which 
was  positive  over  the  whole  range  for  the 
small  initial  tension  disappears  near  the  inner 
positions  for  the  great  initial  tension  (see  points  (37)  and  (38)), 
so  that  the  governor  is  worthless  between  positions  (1)  and 
(2)  for  the  great  initial  tension,  that  is  for  the  high  speed. 

In  this  calculation  it  was  assumed  that  the  variation  of  Q 
is  produced  by  the  tightening  of  the  main  spring  (50)  (Fig.  31), 


ADJUSTMENT  OF   EQUILIBRIUM  SPEED 


53 


but  the  diagram,  and  with  it  the  resulting  variation  of  p, 
remain  just  the  same,  if  the  tightening  of  the  main  spring  is 
replaced  by  the  addition  of  a  weight  to  the  axial  forces,  or  if 
the  main  spring  (50)  of  Fig.  31  is  replaced  by  two  springs 
(51)  and  (52)  (see  Fig.  33),  one  of  which  is  at  rest,  accessible, 
and  is  tightened  for  the  purpose  of  speed  adjustment.  In 
Chapter  IX  proof  will  be  given  that  too  small  a  value  of  p 
(static  fluctuation)  interferes  with  proper  regulation.  In 
Fig.  31  the  static  fluctuation  (as  measured  by  the  tangent 


FIG.  34 


FIG.  35 


to  the  characteristic  at  point  (38) )  has  become  zero  or  even 
negative.  This  condition,  which  arises  in  all  similar  types  of 
governors,  whenever  a  constant  force  is  added  at  the  collar, 
is  serious  enough  to  call  for  some  different  method  of  adjustment. 

Conditions  will  be  better  if  the  added  force  Q  at  the  collars 
varies  with  the  movement  of  the.  latter  in  some  ratio  to  the 
spring  force. 

If  addition  of  mass  is  permissible,  an  arm  (1),  carrying 
a  movable  weight  (2),  may  be  keyed  on  the  rocker  shaft  (3) 
making  angles  ii  or  i2,  etc.  (see  Fig.  34),  with  the  governor 


54       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


lever.  In  this  manner,  the  added  effective  force  is  greater  in 
the  top  position  of  the  collar  than  it  is  in  the  bottom  position, 

force  added  in  top  position 

and  the  ratio  of  —         .  .    .  . — r~  —r~. —  remains   con- 

force  added  in  bottom  position 

stant,  no  matter  what  the  added  force  may  be.  The  angle  i  may 
be  so  selected  that  this  ratio  fits  the  scale  of  the  spring  in  the 
governor  quite  closely. 

In  spite  of  these  static  advantages  the  just  described  method 
is  seldom  used,  because  the  inertia  of  the  sliding  weight  is 
detrimental  to  the  promptness  of  the  governor. 

A  similar  static  advantage  (without  the  drawback  of 
inertia)  is  attained  by  the  use  of  a  " speeder"  with  several 

springs  of  different  free 
lengths,  as  shown  in  Fig.  35. 
Such  a  device  furnishes  a 
load  which  grows  faster  as 
point  (jf)  rises.  Tightening 
up  the  speeder  does  not  add 
a  constant  force,  but  a 
variable  force,  as  may  be 
seen  by  comparing  the  work- 
ing ranges  (3),  (4)  and  (5) 
of  Fig.  36  with  each  other. 
The  same  result  can  be  ob- 
tained by  replacing  the  two 
or  three  springs  with  a  single  volute  (cone-shaped)  spring  ;  it  too, 
as  is  generally  known,  has  the  property  of  a  scale  growing  with  the 
deflection,  because  the  coils  of  larger  diameter  deflect  first  and 
come  up  solid  against  the  stop,  leaving  the  additional  deformation 
to  smaller,  and  consequently  stiff er  coils.  The  number  of  schemes 
which  may  be  employed  for  adjusting  the  speed  of  this  type  of 
governor  is  by  no  means  exhausted  herewith.  It  is  possible 
to  change  lever  arm  and  initial  tension  of  the  speeder  spring 
in  such  a  way  that  the  static  fluctuation  remains  practically 
constant.  Figure  37  illustrates  diagrammatically  such  an  ar- 
rangement. The  parts  drawn  in  heavy  black  lines  move  with 
the  governor  and  swing  about  fixed  point  (4).  Spring  (5) 
which  is  fastened  to  fixed  point  (6)  takes  hold  at  a  point  which 


Motion  of  Point     O 
FIG.  36 


ADJUSTMENT   OF  EQUILIBRIUM   SPEED 


55 


is  movable  relative  to  the  levers.  A  few  positions  (1),(2),(3) 
have  been  indicated  by  dotted  lines.  The  determination  of  the 
proper  location  of  point  (6)  and  of  points  (1)  and  (7)  is  not 
difficult,  but  rather  tedious. 

The  speed  adjustment  of  governors  of  the  Hartnell  type 
has  been  treated  in  detail,  not  because  the  Hartnell  type  de- 
serves special  attention, 
but  because  it  furnishes 


Governor 
Col  lar 


Crosshead  guided  by 
Slots  in  outer  arms 


Fixed  Point 


FIG.  37 


FIG.  38 


an  example  of  how  the  statics  of  speed  adjustment  should  be 
treated  in  any  type  of  governor. 

In  connection  with  speed  adjustment  by  variation  of  axial 
force  Q  three  additional  features  deserve  mention,  namely  : 

(1)  friction  of  governor  collar, 

(2)  detention  by  governor  friction  due  to  forces  at  collar, 

(3)  variations  of  governor  strength  due  to  forces  at  collar. 
(1)  Whenever  forces  are  transmitted  through  a  governor 

collar,  the  latter  becomes  a  step  bearing,  the  location  of  which 
makes  lubrication  somewhat  difficult.  If  lubrication  is  neg- 
lected, heating  and  wear  result.  Ball  and  roller  bearings  have 
given  better  service  in  this  place  than  sliding  bearings.  Figure 
38  shows  a  successful  design. 


56       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


From  the  standpoint  of  avoiding  trouble  with  the  collar 
bearings  it  is  desirable  to  push  up  on  the  collar,  if  great  speed 
changes  are  desired,  because  then  the  heaviest  thrust  is  coupled 
with  the  slowest  speed. 

(2)  Many  of  the  modern  governors  are  so  designed  that 
the  joints  are  free  from  forces  caused  by  centrifugal  action. 

If,  however,  5%  speed 
adjustment  is  desired, 
approximately  10%  of  the 
centrifugal  force  must  be 
transmitted  through  joints 
due  to  the  added  force  at 
the  collar.  In  addition, 
some  force  must  be  trans- 
mitted through  the  collar 
even  at  normal  speed,  if  a 
speeder  spring  is  used,  so 
that  on  an  average  12%  to 
15  %  of  the  centrifugal  force 
must  be  transmitted  through 
the  joints  if  5%  speed  adjust- 
ment is  desired.  This  fact 
should  not  be  overlooked 
with  regard  to  governor 
friction  and  wear  of  joints. 
(3)  Forces  at  the  collar 
affect  the  strength  of  the  governor.  This  is  usually  of  small 
consequence,  except  when  the  axial  force  pushes  up  and  con- 
siderably reduces  the  speed.  In  this  case  the  strength  of  the 
governor  is  very  much  reduced,  and  the  governor  does  not 
handle  valve  gears  offering  great  friction  resistance. 

The  means  mentioned  under  No.  3,  namely,  variation  of 
governor  mechanism,  is  seldom  practiced.  A  brief  description 
of  one  example  will  illustrate  the  principle. 

In  Fig.  39,  (1)  is  the  mass  center  of  a  centrifugal  weight. 
The  weight  is  guided  by  the  vertical  path  of  point  (2)  and  by 
the  gliding  of  surface  (3)  on  roller  (4).  This  latter  path  can 
be  varied  by  the  turning  of  handwheel  (5)  which,  by  means  of 


Sleeve 
slides  up 
and  down 


slngjdoes 
not  revolve 


-  Centrifugal 
weight- 


Revolves  on,  constant 
orbit,  fora  gi'ven 
speed  adjustment 


FIG.  39 


ADJUSTMENT  OF  EQUILIBRIUM   SPEED 


57 


screw  (6)  with  lock  nut  (7),  raises  or  lowers  point  (8).  This 
motion,  by  means  of  revolving  lever  (9)  with  fulcrum  (10), 
moves  roller  (4)  in  or  out.  Radial  displacement  of  weight  (1), 
and  lever  arm  of  centrifugal  force  are  varied  by  this  adjust- 
ment, resulting  in  a  wide  range  of  speed  adjustment;  the  maxi- 
mum mean  speed  is  more  than  twice  the  minimum  mean  speed. 
The  governor  just  described  was  invented  by  Strnad  (Germany). 
Although  the  outward  appearance  of  the  governor  is  simple, 


FIG.  40 

the  interior  is  complicated  and  expensive.    The  joints  transmit 
heavy  forces,  which  means  that  they  are  subject  to  wear. 

Means  No.  4,  namely,  change  of  relative  position  of  governor 
and  power-controlling  mechanism,  is  often  used.  Figure  40 
illustrates  this  method  diagrammatically.  By  means  of  the 
turnbuckle  (2)  the  distance  (4)  (5)  may  be  adjusted.  During 
this  adjustment  the  governor  (jf)  remains  at  first  stationary, 
because  it  is  held  in  equilibrium  between  centrifugal  and  cen- 
tripetal forces.  The  resulting  change  in  the  position  of  the 
power-controlling  device  (3)  unbalances  the  equilibrium  between 
power  generation  and  power  absorption.  Hence  the  speed 


58      GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


varies,  and  the  governor,  in  moving  towards  a  new  position  of 
speed  equilibrium,  shifts   (3)  until  power  equilibrium  is  again 

attained.  If  the  difference  in  speed 
does  not  require  a  difference  in  the 
position  of  controlling  device  (3),  the 
latter  will  return  to  its  original  posi- 
tion; in  all  other  cases  it  will  not 
quite  return  to  that  position.  In  any 
event  the  position  of  governor  (1)  has 
been  changed,  and  with  it  the  speed 
of  the  prime  mover. 

It  is  necessary  to  limit  the  motion 
of  the  controlling  device  (5)  by  stops 
such  as  are  diagrammatically  indicated 
in  (6)  and  (7)  (unless  the  design  of 
said  device  makes  the  use  of  additional 
stops  superfluous),  because  the  position 
of  the  governor  is  not  fixed  relative  to 
the  power-controlling  device. 

The  magnitude  of  the  speed  adjust- 


Enlarqed  detail 
of  Catch  block  - 


FIG.  41 


merit  which  can  be  attained  by  this 

method    depends    upon    the     static 

fluctuation  of  the  governor.     If  it  be 

small,  the  limits  of  speed  adjustment 

must  be  narrow.    If  the  greatest  speed 

of  the  governor  is  several  times  the 

smallest  speed,   very  wide  limits  of 

speed  adjustment  can  be  obtained;  but 

with  high  normal  speed  of  the  prime 

mover  a  removal  of  the  load  produces 

a  dangerously  high  no-load  speed.    To 

insure  safety  under  these  conditions, 

automatic  disconnecting  devices  have 

been  designed  which  disconnect  the 

governor  from  the  power-controlling 

device,    as    soon    as    a    predetermined    maximum    speed   has 

been    reached,    and    release    a    force    which    shuts    off    the 

power.      Figure  41   shows   a  frequently  used   device    of  this 


® 

^ 

.^—  ' 

-—  -*" 

(2 

s 

p*** 

f 

? 

V 

A 

— 

/ 

-  Greatest  Adjustable  Speed 

3 

i- 

- 

1 
.Safety  Travel 

>  _ 

f 

CO 

_L 

Lift 

of  Collar 
FIG.  42 

ADJUSTMENT  OF  EQUILIBRIUM   SPEED 


59 


type; l  the  illustration  represents  a  detail  of  point  (4)  of  Fig.  40. 
As  soon  as  rod  (10),  Figs.  40  and  41,  reaches  a  nearly  horizontal 
position  corresponding  to  the  highest  safe  speed  of  the  governor, 
the  rod  (13)  of  catch  block  (11)  strikes  collar  (14)  and  releases 
the  rod  (15)  carrying  weights  (12).  These  weights,  in  dropping, 
close  the  power-controlling 
valve.  Before  the  engine  can 
be  started  again,  the  rod  (15) 
must  be  lifted  to  again  engage  -j- 
catch  block  (11).  ^ 

The  necessity  of  a  discon- 
necting device  can  be  avoided 
by  a  governor  whose  speed  curve 
has  the  shape  indicated  in 
Fig.  42.  Part  (1)(2)  of  this 
curve  is  used  for  speed  adjust- 
ment, as  described.  Part  (2)  (3) 

used    to    bring    the    power- 


is 

controlling  device  to  no-load 
position  in  case  of  accident. 
Such  a  governor  was  designed 
by  Professor  J.  Stumpf  (Germany).  It  is  shown  in  Fig.  43. 
In  this  governor  skillful  application  is  made  of  variation  of 
leverage  of  main  spring  (3),  and  of  lost  motion  of  spring  (3) 
and  spring  (4)  in  this  manner:  In  the  low  positions  of  collar 
(5)  the  spring  (4)  pushes  upward,  allowing  a  low  speed  to 
raise  the  governor.  Spring  (4)  is  very  short  and  soon  gets 
out  of  action  with  rising  speed.  On  account  of  slots  (6), 
the  main  spring  (3)  is  ineffective  in  the  bottom  part  of  the 
governor  travel.  With  rising  collar  it  takes  hold  and  vastly 
increases  the  equilibrium  speed.  In  the  higher  position  of 
collar  (5)  the  force  of  spring  (3)  increases  slowly,  whereas  its 
lever  arm  L  decreases  rapidly,  which  causes  the  speed  to  change 
very  little  for  the  upper  part  of  the  travel  of  collar  (5). 

Another  governor  with  a  speed  curve  similar  to  that  shown 
in  Fig.  42  is  described  in  Chapter  XII. 

1  This  device,  as  well  as  the  whole  method  No.  4,  was  originated  and  developed 
by  Mr.  K.  Weiss  (Switzerland).  The  method  was  first  used  in  the  United  States 
by  Mr.  B.  Nordberg,  of  Milwaukee,  Wis. 


FIG.  43 


60       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

Governors  of  this  type  are  useful  for  pumping  machinery 
only.  The  modern  tendency  in  such  machinery  is  to  adapt 
the  supply  to  the  demand  and  to  regulate  either  for  constant 
pressure  or  for  constant  rate  of  delivery.  Forces  other  than 
centrifugal  are  used  for  this  purpose.  Speed-changing  gov- 
ernors of  that  type  are,  therefore,  not  considered  in  the  present 
chapter,  but  are  discussed  in  Chapters  XI  and  XII. 

References  to  Bibliography  at  end  of  book:  30,  36,  51,  73. 


CHAPTER   VI 

SHAFT    GOVERNORS 

1.  Forces  Acting  in  Shaft  Governors. —  The  term  "  shaft 
governor"  commonly  denotes  a  governor  the  centrifugal  weights 
of  which  move  in  a  plane  at  right  angles  to  the  axis  of  the  shaft 
or  spindle,  and  which  adjusts  the  position  of  an  eccentric  or 
crank  relative  to  other  revolving  parts.  Figures  4,  5,  8,  9,  44 
illustrate  shaft  governors. 

The  arrangement  of  centrifugal  and  inertia  weights  in  shaft 
governors,  their  method  of  fastening,  the  linkage  between 
weights  and  eccentric,  the  arrangement  of  springs,  and  the 
transmission  of  motion  to  the  valve  gear  belong  in  treatises 
on  machine  design  and  engine  design.  They  do  not  form 
subjects  of  the  present  book. 

Spindle  governors  could  be  studied  apart  from  the  active 
forces  which  the  valve  gear  might  impress  upon  them,  because 
most  spindle  governors  have  to  overcome  mainly  passive  re- 
sistance, compared  to  which  the  small  existing  reaction  is 
usually  of  little  or  no  importance.  Shaft  governors,  on  the 
other  hand,  have  to  move  valves  directly  against  inertia  forces, 
against  varying  friction  forces  and  against  varying  unbalanced 
steam  pressure.  These  forces  react  upon  the  governor  and 
tend  to  disturb  the  equilibrium  between  centrifugal  forces  and 
spring  forces.  Not  only  does  this  reaction  induce  vibration, 
but  it  has  an  "  integrated  effect, "  that  is  to  say,  a  definite 
average  force  or  moment  which  is  added  to  the  spring  moment 
and  changes  the  speed  from  what  it  would  be,  if  that  effect 
were  zero  (see  also  pages  38  and  following).  The  average 
effect  of  the  reacting  force  or  moment  is,  in  practically  every 
shaft  governor,  large  enough  to  upset  static  equilibrium,  and 
must  therefore  be  considered  either  by  theoretical  study,  or 
else  by  experiment. 

In  view  of  these  disturbing  influences,  a  complete  static 
calculation  of  a  shaft  governor  involves  the  following  steps: 

61 


62       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

Select  a  static  fluctuation  p,  about  the  permissible  value 
of  which  see  Chapter  IX,  and  compute  the  various  moments 
tending  to  displace  the  centrifugal  weights,  viz.  centrifugal 
moments  of  all  masses,  moments  due  to  inertia  of  reciprocating 
masses,  due  to  valve  friction,  eccentric  strap  friction,  and  that 
due  to  unbalanced  steam  pressure,  for  three,  or  better,  four 
positions  of  the  weights.  Then  locate  and  dimension  a  spring 
so  that  its  moment  (negatively)  coincides  with  the  sum  of  all 
other  moments.  This  latter  problem  is  not  difficult,  if  the 


FIG.  44 

weight  arms  swing  through  a  small  angle  and  if  the  springs  are 
protected  against  disturbing  deformations  due  to  centrifugal 
force.  If,  however,  the  weight  arms  swing  through  a  large 
angle,  say  more  than  40°,  or  if  the  springs  are  allowed  to  bow 
out  under  the  action  of  centrifugal  force,  no  satisfactory  co- 
incidence of  moments  can  be  attained  with  one  set  of  springs, 
and  unusual  expedients  must  be  resorted  to. 

On  account  of  the  great  variety  of  shaft  governors  on  the 
market,  and  on  account  of  the  still  greater  number  of  valve 


SHAFT   GOVERNORS 


63 


gears  which  they  control,  it  is  impossible  to  follow  out  this 
method  in  all  its  details  within  the  limitations  of  the  present 
book.  It  is,  therefore,  advisable  to  study  the  underlying 
principles  with  the  aid  of  one  particular  example.  The  careful 
study  of  one  example  will  show  the  methods  which  are  to  be 
followed,  with  slight  modifications,  in  all  cases. 

References  to  Bibliography  at  end  of  book:    1,  13,  24,  30,  36,  40,  50,  51,  58,  59, 
68,  73,  74. 

2.  Centrifugal  Moment  of  Rotating  Masses.  —  Figure  44 
shows  a  simple  type  of  governor  suitable  for  study.  This 
governor  is  used  for  controlling 
slide  valves,  including  piston 
valves.  The  triangle  (1}(2}(3)  is 
fixed  relative  to  the  shaft  —  the 
center  of  which  is  (1)  -  -  and 
rotates  with  it.  (4)  is  the  center 
of  the  eccentric  which  is  shifted 
across  the  shaft  by  the  regulating 
forces,  maintaining  an  approxi- 
mately constant  lead  of  the  valve. 
The  centrifugal  weight  (5)  tends 
to  fly  out;  it  is  restrained  prin- 
cipally by  the  spring  (6),  but  to 
some  extent  also  by  the  centrifugal 
force  of  the  eccentric  (4)  and  of  its  strap.  (5)  and  (4)  are  joined 
mechanically  by  link  (7). 

For  the  sake  of  clearness  some  parts  of  the  governor  have 
been  drawn  diagrammatically  in  Fig.  45.  With  the  notations 
of  this  latter  illustration,  the  centrifugal  moment  of  the  small 
mass  dm  about  the  suspension  point  (2)  is  d  Mc  =  dm  r  u2  L. 
But  the  area  of  the  triangle  (1)  (2)  (11}  is  \  r  L  =  |  s  b  which 
makes  the  element  of  the  centrifugal  moment 

d  Mc  =  dm  s  b  u2. 
The  moment  of  the  whole  centrifugal  weight  is 

Mc  =  su2  fdm  b  =  mBsu2 (1) 

where  B  is  the  perpendicular  distance  from  mass  center  of 
weight  (5)  (including  supporting  lever)  to  line  (1)(2),  and  m 


FIG.  45 


64      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

is  the  mass  of  the  centrifugal  weight  (5),  including  lever.  From 
this  equation  follows  the  fact  that  in  shaft  governors  the  dis- 
tribution of  the  mass  around  the  mass  center  of  the  centrifugal 
weight  has  no  influence  upon  the  speed.  In  this  respect  shaft 
governors  differ  from  spindle  governors  (see  paragraph  4  of 
Chapter  III). 

Equation  (1)  applies  to  any  revolving  mass  in  a  shaft 
governor  and  furnishes  the  moment  of  the  mass  about  its  own 
suspension  point.  If  applied  to  the  eccentric,  it  furnishes  the 
moment  of  the  centrifugal  force  of  its  mass  about  point  (3),  of 
Fig.  44,  which,  however,  can  easily  be  converted  into  a  moment 


m 


FIG.  46 

about  point  (2)  by  means  of  the  leverages  of  the  connecting 
linkage. 

The  eccentric  strap  does  not  revolve,  but  each  particle 
describes  a  path  similar  to  an  ellipse  and  exerts  individual 
inertia  forces,  the  integrated  effect  of  all  of  which  is  trans- 
mitted to  the  eccentric  proper.  Generally  speaking,  the  inte- 
gration can  only  be  accomplished  by  a  tedious  point  by  point 
process.  Fortunately,  the  distribution  of  material  in  the  ec- 
centric strap  is  symmetrical  about  the  center  of  the  eccentric 
in  the  vast  majority  of  cases.  The  whole  mass  may  then  be 
considered  as  concentrated  in  the  center  of  the  eccentric  and 
be  added  to  the  mass  of  the  latter. 

3.  Moment  due  to  Inertia  of  Reciprocating  Parts.  —  If 
the  valves  moved  by  the  governor  are  driven  by  a  cam,  the 


SHAFT   GOVERNORS 


65 


Equal 


integrated  effect  of  the  moment  cause  by  their  inertia  can  be 
ascertained  only  by  a  graphical  integration,  but  if  the  valves 
are  operated  directly  by  the  eccentric  with  practically  sine 
harmonic  motion,  the  integral  may  easily  be  found  thus: 

In  Fig.  46,  (1)  is  the  center  of  the  eccentric  and  (3)  is  the 
suspension  point  of  the  eccentric.  (3)  revolves  about  (2), 
which  is  the  center  of  the  shaft.  The  eccentric  reciprocates  a 
mass  mv  (mass  of  the  valve)  by  means  of  long  eccentric  rod 
(1)(4).  The  following  derivation  is  based  upon  the  supposi- 
tion that  mass  mv  is  not  large  enough  to  displace  point  (1) 
perceptibly  from  its  circular  path. 

When  (2)(1)  coincides  in  direction  with  (#)(4),  the  inertia 
force  is  mv  r  u2.  In  the  position  shown  in  the  illustration  it  is 
smaller.  Usually  the  eccentric  rod  (1)(4)  is  very  long  com- 
pared to  the  eccentric  radius  (1)(2).  The  direction  of  the 
inertia  force  is  then  practically  con- 
stant, and  its  magnitude  varies  with  the 
cosine  of  the  angle  j.  If  (1)  (5)  repre- 
sents mv  r  u2,  then  (1)  (6)  =  (/)  (5)  cos  j 
is  the  inertia  force  in  the  position 
shown  in  the  illustration,  and  the  circle 
with  diameter  (1)  (5)  is  the  locus  of  the 
terminals  of  the  force  vectors,  referred 
to  the  rotating  system. 

In  one  revolution  of  the  shaft  the 
just  mentioned  circle  is  passed  over 
twice.  This  will  readily  be  seen  by  a 
study  of  the  forces  existing  when  the 
shaft  has  turned  through  180°,  see 
dotted  position,  because  the  forces  in  the  two  positions  have 
the  same  magnitude  and  direction  relative  to  the  rotating 
system. 

The  average  effect  of  a  force  vector  describing  a  circle  with 
constant  angular  velocity  may  be  found  by  the  following 
reasoning  (see  Fig.  47).  Any  four  vectors  (1)(7),  (-O(tf), 
(1)(9),  (1)(8)>  located  symmetrically  as  shown,  have  the 
average  horizontal  component  (1)(10),  whereas  all  the  vertical 
components  cancel.  Since  the  same  is  true  for  any  four  sym- 


FIG.  47 


66       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

metrically  located  vectors,  (1)(10)  is  the  average  of  all  the 
force  vectors,  both  with  regard  to  magnitude  and  direction. 

Application  of  this  result  to  Fig.  46  means  that  one  half 
of  00(5),  or  (-0(7),  or,  in  symbols,  ^  mv  r  u2,  represents  the 
average  of  the  inertia  forces,  both  with  regard  to  magnitude 
and  direction.  The  same  effect  is  produced  by  a  mass  J  mv, 
located  in  the  center  of  the  eccentric,  and  revolving  with  the 
latter.  The  effect  of  the  inertia  of  the  reciprocating  valve  is, 
therefore,  easily  taken  care  of  by  adding  one  half  of  its  mass 
to  the  rotating  mass  concentrated  at  the  center  of  the  eccentric. 

If  mass  mv  is  big  compared  to  the  masses  swinging  in  the 
governor,  the  path  of  point  (1)  is  no  longer  circular.  The  equa- 


FIG.  48 

tions  of  motion  of  the  point  (1)  then  lead  to  an  elliptic  integral 
which  is  quite  difficult. 

References  to  Bibliography  at  end  of  book:   36,  40,  50,  58,  59,  74. 

4.  Moment  Due  to  Friction  of  Valve  Gear. —  The  average 
reaction  of  valves  having  a  sine  harmonic  motion  may  be 
found  by  a  similar  analysis.  Figure  48  is  a  repetition  of 
Fig.  46  with  the  exception  that  inertia  forces  have  been  re- 
placed by  friction  forces.  If,  as  before,  we  neglect  the  small 
angularity  of  the  eccentric  rod,  the  direction  of  the  friction 
forces  remains  constant;  hence  this  direction  revolves  uni- 
formly with  regard  to  the  rotating  system.  In  Fig.  48  the  fric- 
tion vectors  have  been  entered.  For  a  constant  value  of  the 
friction  force,  the  vector  describes  a  semicircle  (5)  (6)  (2), 


SHAFT   GOVERNORS  67 

jumps  back  to  (5),  again  describes  the  semicircle,  etc.  If  the 
friction  force  is  not  constant,  the  semicircle  is  distorted. 

The  integrated  effect  of  the  friction  force  is  represented  by 
the  average  vector.  In  any  case,  including  that  of  variable 
friction  force,  it  can  be  found  by  graphical  construction.  In 
the  case  of  constant  friction  force  the  terminal  of  the  average 
vector  is  the  mass  center  of  the  semicircular  line  (5)  (6)  (2). 
The  magnitude  of  the  average  vector  is  therefore  2  /TT  times 
the  friction  force.  It  acts  at  right  angle  to  the  diameter  (2)  (1). 

The  integrated  effect  of  friction  and  of  inertia  must  be 
determined  for  several  values  of  the  angle  ft,  that  is  to  say  for 
several  configurations  of  the  governor.  This  is  necessary  for 
the  purpose  of  equating  the  spring  moment  to  the  sum  of  all 
other  moments  over  the  whole  range  of  the  swing  of  the  governor. 

References  to  Bibliography  at  end  of  book:  36,  40,  50,  58,  59,  74. 

5.  Moment  due  to  Friction  between  Eccentric  and  Strap. 
-  Friction  between  eccentric  and  strap  is  produced  by  the 
weight  and  the  centrifugal  force  of  the  strap,  by  the  forces 
transmitted  through  the  eccentric  rod  (valve  inertia,  valve 
friction,  unbalanced  steam  pressure),  and  by  the  pressure  of 
the  assembling  fit  between  eccentric  and  strap.  The  combina- 
tion of  these  forces  for  various  angular  positions  of  the  whole 
governor  and  for  a  few  positions  of  the  parts  in  the  governor 
can  always  be  made  graphically.  The  friction  moment  result- 
ing from  these  forces  is  quite  uncertain,  because  the  coefficient 
of  friction  between  eccentric  and  strap  varies  within  wide 
limits  with  quantity  and  viscosity  of  oil.  It  is  frequently 
observed  that  shaft  governor  engines  have  a  different  speed  at 
starting  up  (when  the  oil  is  cold  and  thick)  from  that  which 
finally  establishes  itself,  after  the  oil  has  been  heated  by  fric- 
tion. Another  uncertainty  is  introduced  by  the  deformation 
of  the  eccentric  straps.  The  latter  are  too  often  designed  so 
weak  that  they  cause  an  amount  of  binding  and  gripping 
sufficient  to  frustrate  any  calculation.  Nevertheless,  a  brief 
account  will  be  given  of  the  distribution  of  frictional  forces 
around  the  eccentric,  because  the  seemingly  erratic  behavior 
of  many  shaft  governors  cannot  be  understood  without  the 
knowledge  of  these  forces. 


08       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


Suspension 
Point 


FIG.  49 


Figure  49  shows  a  governor  eccentric  and  strap  with  the 
principal  forces  acting  upon  them,  and  Fig.  50  illustrates  the 

distribution  of  forces  by  means  of 

oJn 

vectors    having    their    origins   at 
point  (1). 

For  a  given  load,  the  centrif- 
ugal force  of  the  eccentric  strap 
has  a  constant  magnitude  and 
direction  (1)  (2)  relative  to  the 
revolving  eccentric.  Valve  inertia 
is,  in  most  cases,  a  sine  function 
and  adds  the  circle  (2)  (3)  (4)  (5) , 
compare  also  Fig.  46.  The  force 
due  to  valve  friction,  if  the  latter 
be  constant,  is  also  a  circular  func- 
tion and  acts  in  the  same  direction 

as  valve  inertia  ;  but  the  function  is  discontinuous  and  changes 
its  sign  abruptly  at  the  ends  of  the  valve  travel,  see  also  Fig.  48. 
Addition  of  this  force  to  those  previously  enumerated  furnishes 
the  vector  terminal  curve  (6)  (7)  (8)  (9)  (2).  The  weight  of 
the  eccentric  strap  is  constant  in  magnitude  and  in  absolute 
direction,  and,  there- 
fore, rotates  contin- 
uously around  the  re- 
volving eccentric. 
The  same  is  true  of  un- 
balanced steam  pres- 
sure, unless  the  latter 
be  variable.  The  re- 
sultant of  strap  weight 
and  of  steam  pressure 
changes  the  final  locus 
of  the  terminus  of  the 
force  vector  to  the  curve  (14)  (13)  (12)  (11)  (10)  (15)  (16}  (17) 
(18)  (14),  etc.  Thus  (1)(12)  is  a  vector  picked  out  at  random. 
The  correct  method  of  finding  the  average  friction  moment 
from  these  forces  would  consist  in  determining  the  friction 
moment  for  each  force  vector  and  then  averaging  the  friction 


FG.  50 


SHAFT   GOVERNORS  69 

moments  thus  found.  This  method  would  be  tedious  and  is 
entirely  out  of  place  in  view  of  the  uncertainties  with  regard 
to  the  coefficient  of  friction.  Since  the  vectors  sweep  over  a 
small  part  of  the  circumference  of  the  eccentric  only,  the  friction 
moment  caused  by  the  average  vector  coincides  nearly  enough 
with  the  true  average  friction  moment  for  all  practical  pur- 
poses, which  leads  to  the  following  approximative  construction. 
In  Fig.  49  lay  off  (1)(2)  equal  to  centrifugal  force  of  strap 
in  the  direction  from  center  of  shaft  to  center  of  eccentric.  In 
the  same  direction  lay  off  (2)  (20}  equal  to  maximum  inertia 
force  of  reciprocating  valve  parts,  reduced  to  the  center  of  the 
eccentric.  At  right  angle  to  this  direction,  and  opposite  to 
the  direction  in  which  point  (1)  rotates  about  the  center  of 
the  shaft,  lay  off  (20)  (19)  equal  to  64%  of  the  constant  valve 
friction  force  (2/?r  =  .64).  Then  (1)(19)  is  the  average  vector 
and  acts  upon  the  eccentric  at  point  (21).  The  product  of 
this  average  force,  the  friction  coefficient  and  the  lever  arm  6 
furnishes  the  average  friction  moment  for  the  position  under 
consideration. 

References  to  Bibliography  at  end  of  book:  36,  40,  50,  58,  59,  74. 

6.  Spring  Moment.  -  -  The  spring  in  a  shaft  governor  must 
be  of  such  size,  and  must  be  so  located,  that  the  equilibrium 
speed  of  the  governor  (when  governing  the  engine)  rises  gradu- 
ally and  steadily  from  full-load  position  to  no-load  position 
under  any  conditions  of  careful  operation,  with  the  exception 
of  the  first  minute  or  two  after  starting.  A  few  additional 
exceptions  due  to  tangential  inertia  or  to  compensating  oil 
pots  will  be  dealt  with  later  on. 

For  the  purpose  of  expressing  this  rather  general  statement 
in  a  more  tangible  form,  let  us  equate  the  spring  moment  to 
the  rest  of  the  moments. 

Let  M ,  =  spring  moment 

Mc  =  any  one  of  the  speed  moments  (centrifugal,  valve 

inertia) 

Mf  =  any  one  of  the  moments  due  to  friction. 
For  equilibrium,  the  spring  moment  must  balance  all  other  mo- 
ments, so  that  M8  =  S  Mc  +  S  Mf 


70       GOVERNORS  AND  THE   GOVERNING   OF   PRIME   MOVERS 

where  S  is  the  mathematical  sign  for  "the  sum  of."     S  Mc 
means  the  sum  of  all  speed  moments. 

The  speed  moments  are  all  of  the  form  m  r  L  u2,  see  para- 
graph 2  of  present  chapter.  Those  friction  moments  which 
are  caused  by  the  friction  produced  by  centrifugal  forces  are 
of  the  form  fm'  r'  L'  u2,  where  /  is  a  coefficient  of  friction.  All 
other  friction  moments  are  of  the  form  F  I,  where  F  is  a  friction 
force  which  is  practically  independent  of  the  angular  velocity  u. 
By  substitution  of  these  values  we  obtain 

Ms  =  u2[2mrL  +  2fm'r'  L'^  +  ZFl  ......  (1) 


In  order  to  see  clearly  the  conditions  which  the  spring 
moment  must  meet  in  order  to  make  u  rise  steadily,  let  us 
solve  the  equation  (1)  for  u. 


It  is  immediately  seen  that  the  greatest  obstacle  to  securing 
a  gradual  and  steady  rise  of  u  is  the  variability  of  the  friction 
coefficient,  which  affects  both  2  F  I  and  2  /  m!  r'  L'  .  In  practice, 
lubrication  varies;  friction  of  valves  and  stuffing  boxes  varies 
not  only  with  lubrication,  but  also  with  steam  pressure,  steam 
temperature,  tightening  of  packing  bolts  by  engineers,  and  with 
other,  but  minor,  features.  The  variation  of  friction  moment 
affects  u  the  more,  the  smaller  Ms  and  2  m  r  L.  Vice  versa, 
the  greater  Ms  and  S  m  r  L  for  a  given  engine,  the  smaller  the 
disturbances  caused  by  changes  in  friction  forces.  The  latter 
thought,  namely  to  make  the  spring  moment  and  the  centrif- 
ugal moment  quite  great,  is  carried  into  practice  by  all  builders 
of  small  engines  using  shaft  governors.  For  small  and  medium 
sized  engines  the  magnitude  of  the  spring  moment  required  for 
faultless  operation  under  all  conditions  is  seldom,  if  ever,  de- 
termined by  calculation,  but  by  practical  tests. 

Both  calculation  and  experience  prove  that  with  those 
shaft  governors  in  which  the  spring  forces  are  transmitted  to 
the  centrifugal  weights  through  pins,  there  exists  for  each 
engine  a  certain  point,  above  which  an  increase  of  spring  moment 
does  more  harm  than  good,  because  the  friction  in  the  governor 


SHAFT  GOVERNORS  71 

pins  becomes  so  great  that  the  reacting  or  impressed  forces 
coming  from  the  valve  gear  cannot  keep  the  governor  vibrating 
or  " limbered  up"  (see  also  Chapter  VIII).  The  governor 
becomes  sluggish  and  does  not  respond  quickly  to  changes  of 
load.  This  undesirable  feature  can  be  avoided  by  placing  the 
centrifugal  mass  directly  on  the  spring  (see  Fig.  54),  or  by  the 
proper  arrangement  of  inertia  masses. 

The  doubly  beneficial  influence  of  tangential  inertia  in 
shaft  governors  was  recognized  at  a  comparatively  early  time 
in  the  history  of  such  governors.  First,  tangential  inertia 
steadies  the  governor  against  impressed  forces  reacting  from 
the  valve  gear  (see  Chapter  VIII)  ;  and  second,  it  prevents 
racing  and  hunting  no  matter  whether  the  speed  drops  off  as 
the  load  comes  on,  or  whether  it  rises  (see  paragraph  3  of 
Chapter  IX).  The  latter  effect  of  tangential  inertia  was  ex- 
ploited to  obtain  reversed  speed  curves  (higher  speed  at  full 
load  than  at  no  load),  but  the  use  of  "  we-don't-care-what-the- 
speed-curve-is  "  governors  on  engines  driving  alternators  brought 
stern  realization  of  the  fact  that,  at  least  for  the  purpose  of 
driving  alternators  in  parallel,  a  gradual  and  steady  rise  of 
the  speed  is  required  as  the  load  drops  off,  and  that  every 
other  arrangement  is  a  positive  failure.  One  firm  after  another 
had  this  (often  quite  expensive)  experience,  between  the  years 
1900  and  1905..  The  result  is  that  the  statement  made  above 
concerning  a  sufficiently  great  spring  moment  to  maintain  a 
steady  speed  rise  in  spite  of  reasonable  variations  of  friction 
holds  good  for  all  present-day  shaft  governors. 

In  view  of  this  explanation,  it  will  pay  to  make  the  follow- 
ing comparatively  simple,  although  rather  tedious,  calculation, 
whenever  a  new  size  or  type  of  shaft  governor  is  to  be  built. 
For  all  friction  forces  assume  maximum  and  minimum  values 
within  reasonable  limits.  For  guidance  in  this  assumption 
the  coefficient  of  friction  may  be  varied  from  the  low  value  of 
|  %  to  the  high  value  of  12  %.  Compute  the  friction  moments 
with  both  of  these  values  for  three  or  four  positions  (configura- 
tions) of  the  governor,  as  indicated  in  paragraphs  4  and  5  of 
the  present  chapter,  and  substitute  in  equation  (2).  In  either 
case  u  must  rise  gradually  from  full  load  to  no  load.  If  it  does 


72       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


Centrifugal 
.Weight 


not,  either  the  static  fluctuation  p,  or  the  spring  moment  Ms, 
must  be  increased,  or  else  the  location  and  arrangement  of  the 
spring  must  be  changed,  as  explained  below. 

The  rapid  growth  of  the  steam  turbine  in  central  stations 
limits  the  use  of  shaft  governors  for  close-regulation  alternating- 
current  work  more  and  more.  For 
that  reason  a  detailed  example  of 
the  above  outlined  calculation 
would  benefit  only  very  few  readers. 
It  is,  therefore,  omitted. 

The  following  brief  remarks  will, 
however,  be  of  interest.  Each 
speed  moment,  if  plotted  against 
angle  of  swing  of  governor  weight, 
is  part  of  a  slightly  distorted  sine 
curve.  The  distortion  is  caused  by 
the  fact  that  the  governor  is  not 
isochronous.  The  spring  moment  can  never  be  made  to  be  a 
sine  curve,  because  both  spring  force  and  its  lever  arm  vary,  as 
the  governor  moves  in  or  out.  Consequently,  it  is  quite  difficult 
to  make  the  spring  moment  coincide  with  the  sum  of  the  other 
moments  as  required  by  a  gradually  and  steadily  rising  speed, 
if  either  the  main  centrifugal  mass  or  the  eccentric  turns 


FIG.  51 


FIG.  52 

through  a  large  angle.  Large  in  this  case  means  more  than  50°. 
If  the  main  centrifugal  mass  is  large  compared  to  the  influence 
of  other  moments,  and  swings  through  an  angle  not  exceeding 
30  °,  the  problem  of  securing  a  steadily  rising  speed  is  very 
easily  solved.  This  feature  deserves  consideration  in  the  design 
of  new  shaft  governors. 

As  an  illustration  of  the  complications  introduced  by  the 
swinging  of  weights  or  eccentrics  through  large  angles,  the  well 


SHAFT  GOVERNORS 


73 


Roller 


known  Thompson  governor  of  the  Buckeye  Engine  Co.  may 
be  cited.  The  eccentric  is  turned  through  about  110°  on  the 
shaft,  so  that  the  spring  must  balance  a  moment  which  is 
roughly  of  the  form  K  sin  i  +  K'  sin  (3  i  +  if),  where  i  is  the 
angle  through  which  the  lever  arm  (carrying  the  centrifugal 
weight)  swings.  For  many  years  after  its  introduction,  this 
governor  was  not  fit  for  close  regulation.  It  was  made  fit  by 
the  addition  of  auxiliary  springs  which  oppose  the  main  springs 
in  the  inner  position 

of  the  governor  and  Fixed 

go  out  of  action 
somewhere  near  the 
central  position  of 
the  weights.  Even 
with  this  ingenious 
expedient,  the 
governor  is  sensitive 
to  changes  of  fric- 
tion in  eccentric  and 
piston  valves. 

In  the  detail 
calculation  of 
springs  of  shaft 
governors  many 
influences  which,  at  first  thought,  seem  too  trivial  to  have 
much  effect,  must  be  considered.  Among  them  is  the  in- 
fluence of  the  mass  of  the  governor  springs.  Not  only  does 
the  spring  exert  a  centrifugal  moment  which  must  be  taken 
care  of  in  the  balancing  of  the  various  moments,  but 
frequently  the  centrifugal  force  distorts  the  spring  so  that 
both  its  force  and  its  line  of  action  are  altered.  This  condi- 
tion is  illustrated  in  Fig.  51.  The  system  (2)  (3)  (4)  (5) 
rotates  rigidly  about  point  (3).  Roller  (5)  keeps  the  spring 
from  bowing  out.  If  this  roller  is  removed,  the  center  line 
of  the  spring  assumes  a  parabolic  shape  as  indicated  in  an 
exaggerated  manner  by  the  dotted  line  (1)(4\  The  centrif- 

W 

ugal  force  tending  to  bow  the  spring  out  is  —  s  u2,  where  W  is 

the  weight  of  the  spring.    The  meaning  of  s  is  clear  from  Fig.  51. 


Fixed 


FIG.  53 


74      GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


If  S  is  the  elastic  force  and  I  the  length  of  the  spring  before, 
and  Sf  and  I'  the  corresponding  values  after  bowing  out,  then 

Sf      V 

—  =  — ;   but  V  is  found  from  the  relation  that  the  center  line 

0  / 

of  the  spring  becomes  an  arc  of  a  composite  curve  which  is 
so  shallow  that  it  can  be  replaced  by  a  parabola.  Hence 
I'  =  1(1  +  i  i2)}  where  i  follows  (see  Fig.  52)  from  the  relation 

W  su2 

1  =  — T— ;-.     From  these  relations  both  change  of  spring  force 

Q  *  & 

and  change  of  lever  arm  can  be  computed. 

In  modern  shaft  governors 
for  poppet  valve  engines  with 
lay  shafts  it  is  customary  to 
place  the  springs  just  as  close 
to  the  shaft  as  possible  (see 
Fig.  53).  The  centrifugal  force 
of  the  spring  in  this  case  is  so 
small  as  to  be  without  noticeable 
effect. 

Centrifugal  force  of  the 
spring  also  has  a  component  in 
the  direction  of  the  spring. 
However,  the  influence  is  small 
and  can  be  taken  care  of  by 
adjustments  described  below. 

In  some  of  the  best  shaft 
governors,  leaf  springs  are  used. 
If  the  spring  is  held  as  indicated  in  Fig.  54,  the  nature  of  the 
fastening  is  somewhat  uncertain.  It  is  common  to  figure  the 
spring  as  if  it  were  a  cantilever,  built  in  at  point  (2)  and  loaded 
at  point  (1).  Actually  it  is  held  at  points  (2)  and  (3)  and  can 
deflect  between  these  points.  This  feature  should  be  taken  care 
of  in  the  calculation.  The  spring  is  a  beam  which  is  semi- 
constrained  at  (3),  supported  at  point  (2)  and  loaded  at 
point  (1).  While  an  exact  mathematical  solution  may  be  diffi- 
cult, careful  judgment  allows  a  very  close  approximation. 

The  exact  predetermination  of  all  forces  in  a  shaft  governor 
places  an  enormous  amount  of  work  on  the  engineering  depart- 


FIG.  54 


SHAFT   GOVERNORS  75 

ment.  For  that  reason  it  is  often  preferable  not  to  be  quite 
so  particular  in  the  calculations,  but  to  allow  for  all  kinds  of 
adjustments;  so  that  the  man  in  the  field  can  work  out  his 
own  salvation.  Although  the  foregoing  explanations  contain 
the  principles  upon  which  all  adjustments  should  be  based, 
the  effects  of  the  more  important  adjustments  will  be  briefly 
considered. 

(1)  Change  of  spring  tension.     A  change  of  initial  spring 
tension   is   equivalent    to    adding   or    subtracting    a    constant 
spring  force  throughout  the  range  of  governor  motion    (with 
the  exception  of  the  disturbance  caused  by  the  centrifugal 
force  of  helical  springs).    An  increase  of  spring  tension  increases 
the  speed,  but  decreases  stability  and   static  fluctuation;    a 
decrease  of  spring  tension  decreases  speed  but  increases  static 
fluctuation  and  stability. 

(2)  Change  of  spring  leverage.     If  the  movable  end  of  a 
helical  spring  is  shifted  along  the  weight  arm  in  such  a  way 
that  its  tension  in  mid-position  of  governor  is  not  altered,  the 
spring  moment  changes  directly  as  the  spring  leverage.     The 
change  in  spring  moment  necessitates  a  corresponding  change 
of  centrifugal  moment,  which  means  a  change  of  equilibrium 
speed.     A  greater  spring  leverage  works  the  spring  through  a 
wider  range  of  deflection,  which  means  a  greater  variation  of 
spring  moment  between  full-load  position  and  no-load  position, 
or  briefly  an  increase  of  static  fluctuation  and  of  stability. 

It  is  possible  to  locate  a  slot  in  the  weight  arm  in  such  a 
way  that  while  the  spring  leverage  is  increased,  its  tension  is 
decreased,  with  the  result  that  the  speed  of  the  engine  is  not 
varied  by  the  adjustment.  In  this  case  only  the  stability  and 
static  fluctuation  are  varied,  the  speed  remaining  constant. 

In  practice  a  variation  of  spring  tension  is  a  good  deal  easier 
than  variation  of  the  spring  leverage,  because  it  calls  simply 
for  the  adjustment  of  the  tension  screw,  whereas  it  is  necessary 
to  slacken  the  spring  almost  all  the  way  in  order  to  shift  it 
along  the  lever.  Slight  variations  in  speed  are  therefore  mostly 
accomplished  by  variation  of  spring  tension.  Engineers  know 
that  practice  bears  out  theory,  because  by  increasing  spring 
tension  farther  and  farther  they  "strike  a  racing  point,"  which 
necessitates  an  increase  of  spring  leverage. 


76       GOVERNORS  AND    THE  GOVERNING   OF   PRIME   MOVERS 

(3)  Adjustment  of  fixed  end  of  spring  in  a  circular  slot, 
concentric  with  point  of  attachment  of  movable  end  of  spring 
in  mid-position  of  governor  (see  Fig.  55).  This  has  the  effect 
of  varying  the  lever  arm  of  the  spring  for  a  given  position  of 

the  governor  and  of  varying 
the  ratio  of  lever  arms  in  the 
full-load  and  no-load  posi- 
tions. This  adjustment 
offers  very  good  means  for 
making  the  spring  moment 
balance  all  other  moments 
with  a  steady  speed  curve 
throughout  the  range  of 
governor  motion,  unless  the 
angle  of  swing  be  too  great. 
(4)  Adjustment  of 
quantity  of  centrifugal  mass. 
From  equation  (2)  of  this 
paragraph  it  follows  that 

addition  of  centrifugal  weight  (increase  of  ra)  reduces  the  speed, 
and,  vice  versa,  that  reduction  of  centrifugal  mass  means  an 
increase  of  speed.  From  the  same  equation  it  follows  that  the 
stability  and  static  fluctuation  remain  unchanged  only  on  condi- 
tion that  each  and  every  centrifugal  mass  is  changed  in  the 
same  ratio  (not  only  the  so-called  centrifugal  weight). 

There  exist  additional  adjustments  which  the  man  in  the 
field  can  make.  Among  them  are  :  shifting  the  mass  center  of 
one  or  more  of  the  centrifugal  weights;  changing  the  number 
of  active  leaves  or  coils  in  a  spring ;  bringing  into  action  an 
auxiliary  spring  for  part  of  the  travel ;  and  others.  However, 
any  one  of  these  adjustments  should  not  be  made  blindly, 
without  full  knowledge  of  the  theoretical  effect  which  they 
have.  They  should  be  tried  only  after  thorough  discussion 
with  the  designing  engineer.  Adjustments  of  oil  gag  pots  and 
friction  brakes  are,  of  course,  frequently  made.  For  such  ad- 
justments see  the  chapter  on  cyclical  vibrations  of  governors. 

References  to  Bibliography  at  end  of  book:  36,  40,  50,  61,  58,  59,  74. 


CHAPTER  VII 

NATURAL  PERIOD  OF  VIBRATION  OF  A  CENTRIFUGAL  GOVERNOR 

IN  paragraph  2  of  Chapter  III  that  force  was  discussed 
which  returns  a  stable  governor  to  its  position  of  equilibrium, 
after  the  governor  has  been  displaced  from  that  position.  From 
Fig.  17  it  follows  that  the  restoring  force  is  proportional  to 
the  displacement,  so  that  the  frictionless  governor  makes  sine 
harmonic  vibrations  about  the  position  of  equilibrium.  In 
reality  these  vibrations  are  more  or  less  damped,  the  damping 
depending  upon  the  internal  friction  of  the  governor.  From 
mechanics  the  fact  is  known  that  solid  friction  does  not  change 
the  period  of  vibration. 

In  general,  the  natural  vibrations  of  a  governor  are  of  no 
importance.  They  become  of  importance  if  their  period  coin- 
cides, or  nearly  coincides,  with  that  of  the  forces  impressed  upon 
the  governor  by  the  valve  gear.  Knowledge  of  the  natural 
period  is  also  necessary  for  determining  the  stability  of  regula- 
tion. In  order  to  prepare  for  these  interactions  between 
governor  and  prime  mover,  a  method  will  now  be  given  for 
computing  the  period  of  natural  vibrations. 

From  mechanics  the  time  of  a  complete  vibration  is  known 
to  be 

T     =  0  _  %/  vibrating  mass 


restoring  force  per  unit  displacement 

In  this  equation  both  the  vibrating  mass  and  the  restoring 
force  must  be  referred  to  the  same  representative  point.  If, 
for  instance,  the  restoring  force  is  measured  in  the  direction 
of  centrifugal  force  at  the  mass  center  of  the  revolving  weights, 
the  motion  of  all  governor  masses  must  be  referred  to  that 
direction  and  to  that  point.  If,  on  the  other  hand,  the  mass 
motion  is  referred  to  the  governor  sleeve,  the  restoring  force 
must  also  be  referred  to  the  sleeve.  For  the  method  of  such 
reduction  see  below. 

77 


78      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

From  paragraph  2  of  Chapter  III  the  restoring  force  per 

2  C  v 
unit  displacement  is  known  to  be   •          •  for  a  straight-line 

characteristic.  If  the  characteristic  is  curved,  p  is  taken  from 
the  tangent  to  the  characteristic,  as  previously  explained,  at 
the  position  of  equilibrium.  The  vibration  takes  place  about 
the  latter  position.  Substitution  of  the  restoring  force  furnishes 

2M*Vri) (i) 

pC 

In  this  equation  me  is  the  equivalent  mass.  The  method  of 
finding  the  equivalent  mass  is  illustrated  by  Fig.  56,  in  which 
two  closely  adjacent  positions  of  a  governor  have  been  drawn. 
If  for  the  present  only  the  weights  Q l  and  W  are  considered,  the 
equivalent  mass  is 


W 

9  r 

The  square  of  the  travel  results  from  the  double  effect  that 
first  the  greater  travel  requires  greater  accelerating  force  and 
that  second  this  force  acts  with  a  longer  lever  arm. 

If  all  forces  and  mass  motions  of  a  governor  are  referred 
to  radial  direction,  the  equivalent  mass  me  for  any  system  of 

•Sra(ds)2 
masses  is  given  by  the  equation  me  =  — 7T\z — >  where  m  is  any 

mass  in  the  system  and  ds  is  the  space  through  which  it  travels, 
while  the  centrifugal  mass  travels  dr  radially.  In  any  governor 
the  value  of  me  may  be  expressed  by  the  angles,  lengths  of  arms, 
etc.,  but  it  is  usually  easier  to  use  the  method  indicated  above, 
that  is  to  say,  take  the  travels  directly  from  two  positions  of 
the  governor. 

If  a  governor  is  connected  to  a  valve  gear,  its  period  of 
vibration  changes,  because  the  mass  of  the  valve  gear  parts 
has  to  swing  with  the  governor  and  enters  into  the  sum  of  all 
masses  times  travel  squared. 

As  an  example,  the  time  of  vibration  of  the  loaded  Watt 
governor  shown  in  Fig.  56  will  now  be  computed. 

i  Q  =  weight  of  |  counterpoise. 


NATURAL   PERIOD  OF  VIBRATION  OF  A  GOVERNOR  79 


10ADED  WATT  GOVERNOR 
(Calculation  for  ^Governor) 

Weight  of  one  ball-—  ......  -----  W-127  pounds 

Weight  Of  <entcrwt*5leeve»rod5         Q  ,',  34  £ounds 

Length  of  lever  ---------  |=   21" 

......  l,=    14ft" 

......  lz«    |l!/2" 

Lift  of  Collar  ---------  5=  3/4" 

Dead  weight  of  oil-pot  parts  -----  =    22* 

Static  Fluctuation  -----  p* 


Governor  built  forn*RPM=80 


Calculation: 
Cwl  P=  Strength  of  Governor— 

fmaojinary  force  to  be  exerted  on 
collar  to  balance  centrifugal 
force  of  balls. 


,  r,'l.3?6Ft.  C,= 408  pounds 
Measured  r  |.234Ft.  <>348  pounds 
in  d,agram  r;. 


FIG.  56 


80       GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

For  this  governor,  the  equivalent  mass  reduced  to  radial 
travel   (from  p.  78,  equation  2)  equals 

254  X  3.382  +  268  X  3.252  pounds  sec2. 

32.2  X  2.52  ~1T~ 

This  expression  gives  a  mean  value,  because  finite  paths  Dr, 
Ds  and  Dh  have  been  used  instead  of  the  corresponding  dif- 
ferentials dr,  ds  and  dh. 

From  p.   31   the  restoring  force  per  unit  displacement  is 
/7  C*        C* 

known  to  be  z  =  -  -  —  — ,  or  z  =  tan  k  —  tan  i  (Fig.  16),  where 
a  r       r 

k  is  the  angle  which  the  tangent  to  the  characteristic  curve 
makes  with  the  base  line,  and  i  the  angle  which  the  straight 
line  drawn  from  the  same  point  of  tangency  to  the  origin  makes 
with  the  base  line.  The  tangents  are  obtained  by  forming  the 
ratios  of  the  drawing  lengths  of  the  two  short  sides  in  the  right 
angle  triangles  and  by  multiplying  each  length  by  its  scale. 
Thus  we  obtain: 

z  =  -^-  —  -r-^r  =  340  pounds  per  ft.  of  radial  displacement. 

.OO  1..4O 

By  substitution  we  obtain  the  period  of  vibration 

Tn=2w\/—=  6.28  i/H  =  1.82  seconds. 
z  340 

References  to  Bibliography  at  end  of  book:  14,  36,  37,  83. 


CHAPTER  VIII 

EFFECTS  OF  OUTSIDE  FORCES  IMPRESSED  UPON  GOVERNORS 

1.  Resistibility. —  The  power-controlling  mechanisms  which 
are  adjusted  by  governors  may  be  broadly  divided  into  two 
classes,  namely 

(1)  Devices  which  offer  passive  or  friction  resistance  only 
to  the  governor, 

(2)  Devices  which  react  upon  the  governor  and  tend  to 
cyclically  displace  it  from  its  position  of  equilibrium. 

The  features  of  the  governor  which  are  valuable  in  dealing 
with  the  first  class  of  mechanisms  are  strength,  work  capacity, 
and,  for  certain  cases,  tangential  inertia,  see  Chapter  II. 

The  feature  which  is  valuable  in  dealing  with  the  second 
class  of  mechanisms  has  not  received  much  attention  from 
writers  and  has,  therefore,  no  recognized  name  in  any  language. 
Since  the  feature  in  question  is  the  ability  to  resist,  I  have 
adopted  the  term  "resistibility."  Dr.  Proell  uses  the  term 
" moment  of  resistance"  for  shaft  governors. 

The  necessity  for  this  property  in  governors  subjected  to 
great  reaction  will  easily  be  realized.  Heavy  intermittent 
forces  from  the  valve  gear  throw  a  light  governor  back  and 
forth,  causing  unequal  and  irregular  power  distribution,  and, 
consequently,  great  speed  fluctuations.  And  yet  the  light, 
but,  in  this  case,  useless  governor  may  be  very  strong,  because 
the  strength,  in  the  sense  of  paragraph  1  of  Chapter  II  depends 
upon  m  r  u1;  and  r  u2  may  be  very  great,  offsetting  the  small- 
ness  of  m.  It  will  presently  be  shown  that  resistibility  is  indeed 
closely  related  to  the  mass  of  a  governor. 

Returning  to  the  statement  that  light  governors  are  thrown 
back  and  forth  under  the  influence  of  vibratory  forces,  we  are 
forced  to  admit  that  the  actual  motion  of  such  a  governor  is 
not  amenable  to  mathematical  treatment,  except  through 
repeated  semigraphical  point-by-point  integration,  which  is, 

81 


82      GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

of  course,  too  slow  for  any  practical  purpose.  The  difficulty 
is  partly  caused  by  the  interaction  of  governor  and  prime  mover. 
Any  motion  of  the  governor  affects  the  speed  of  the  prime  mover, 
and  variation  of  the  speed  moves  the  governor.  This  motion 
is  superposed  over  the  cyclical  vibration  impressed  upon  the 
governor  by  the  valve  gear.  The  latter  motion  is  modified  by 
the  natural  vibration  of  the  governor  (see  Chapter  VII)  and 
by  the  resistance  of  solid  and  liquid  friction.  From  these  facts 
it  is  evident  that  an  analytical  solution  of  the  problem  of  finding 
the  motion  of  the  governor  is  out  of  question. 

Fortunately,  a  complete  solution  of  this  problem  is  not 
needed  for  practical  purposes.  Since  it  is  not  permissible  to 
have  governor  motions  of  such  a  magnitude  that  they  disturb 
power  distribution  and  vary  the  speed  of  the  prime  mover, 
governors  must  be  made  resistant  enough  to  prevent  excessive 
vibrations,  and  the  influence  of  such  speed  variations  may,  in 
consequence,  be  omitted  from  the  study  of  cyclical  governor 
vibrations.  The  problem  then  is  to  make  governors  resistant 
enough  to  limit  vibrations  (caused  by  reacting  forces)  to  a 
small  fraction  of  the  swing  or  travel  of  the  governor  parts.  For 
the  solution  of  this  problem  the  knowledge  of  certain  facts  con- 
cerning vibrations  is  required.  For  that  reason  they  will  be 
briefly  reviewed. 

If  a  mass  is  subjected  to  a  cyclically  fluctuating  force,  and 
is  not  affected  by  any  other  force,  it  performs  a  vibration  which 
can  easily  be  computed  in  every  detail.  It  is  called  the  im- 
pressed vibration.  Mass  furnishes  the  only  opposition  limiting 
the  amplitude  of  the  impressed  vibration.  The  impressed 
vibration  is  modified  by  friction,  both  liquid  and  solid,  and  by 
the  natural  vibration.  The  latter  may  magnify  or  diminish 
the  amplitude  of  the  impressed  vibration,  depending  upon  the 
ratio  of  their  frequencies.  If  that  ratio  is  near  one,  and  if 
there  is  very  little  friction,  very  large  amplitudes  result.  As  a 
matter  of  fact,  governors  with  very  small  friction,  when  used 
in  connection  with  reacting  valve  gears,  have  occasionally 
struck  that  coincidence  of  frequencies  which  in  mechanics  is 
called  resonance.  Under  such  conditions  a  frictionless  governor 
is  useless  and  friction  must  be  added  to  make  it  useful,  usually 


EFFECTS  OF   OUTSIDE  FORCES  83 

much  to  the  dismay  of  the  designer  who  tried  to  produce  cor- 
rect regulation  by  the  use  of  a  frictionless  governor.  Fortu- 
nately, a  relatively  small  amount  of  friction  suffices  to  prevent 
undue  magnification  of  the  impressed  amplitude. 

In  paragraph  2  of  Chapter  IX  proof  is  furnished  that  a 
certain  amount  of  friction  is  needed  in  any  governor  to  insure 
stability  of  regulation.  And  such  an  amount  of  friction  is  needed 
that  resonance  (magnification  of  impressed  amplitude)  cannot 
occur,  if  regulation  is  to  be  stable.  For  this  reason  resonance 
may  also  be  dismissed  from  the  discussion. 

There  remains  then  only  the  amplitude  of  the  impressed 
vibration,  damped  by  solid  and  liquid  friction.    Friction  reduces 
the  amplitude  of  any  vibration  and  thus  increases  resistibility. 
This  brings  up  the  question  to  what  extent  friction  should  be 
depended  upon  to  furnish  resistibility.    No  generally  applicable 
answer  can  be  given,  for  the  following  reasons:    The  amount 
of  friction  which  is  necessary  in  a  governor  to  produce  stability 
of  regulation  varies  with  the  promptness  of  the  governor  and 
with  the  kinetic  energy  stored  up  in  the  rotating  masses  of  the 
prime  mover  per  horse  power  of  capacity  (see  paragraph  2  of 
Chapter  IX).  A  considerable  increase  of  friction  over  the  amount 
which  is  necessary  for  stability  of  regulation  does  harm,  because 
it  delays  the  governor,  when  the  latter  is  adjusting  the  power- 
controlling  mechanism  after  a  change  of  load,   and  thereby 
causes  undue  and  excessive  speed  fluctuation.    This  uncertainty 
of  the  permissible  amount  of  frictional  damping  in  governors 
makes  it  advisable  to  depend  mainly  upon  mass  for  keeping 
down  the  amplitude  of  cyclical  vibrations  and  to  depend  upon 
friction  to  a  limited  extent  only.     If  a  rule  is  wanted,  the  fol- 
lowing will  serve  as  a  rough  guide.     Use  a  governor  with  suf- 
ficient mass  to  reduce  the  amplitude  of  the  impressed  vibration 
to    1J   times   the   permissible   amplitude,    and   obtain   further 
reduction  of  amplitude  by  solid  or  liquid  friction.     Just  what 
amplitude    is    permissible    will    be    considered    in    the    next 
paragraph. 

Solid  friction  is  very  effective  as  a  damping  agent;  however, 
several  precautionary  measures  must  be  observed  to  make  its 
use  successful.  In  governors,  such  as  shown  in  Figs.  2  and  4, 


FIG.  57 


84      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

great  centrifugal  forces  are  transmitted  through  the  pin  joints. 
The  diameters  and  lengths  of  these  pins  are  usually  made  very 
small  for  the  purpose  of  reducing  friction,  and  the  joints  wear 
considerably,  if  the  governor  vibrates.  It  is,  therefore,  much 
better  to  make  the  pressure  between  the  rubbing  surfaces  so 
small  that  wear  is  very  slow.  Furthermore,  it  is  advisable  to 
make  the  friction  adjustable  and  to  arrange  the  parts  so  that 
slight  wear  does  not  noticeably  vary  the  fric- 
tion. Finally,  it  is  desirable  to  keep  oil  away 
from  the  rubbing  surfaces,  so  that  a  varying 
amount  of  oil  may  not  disturb  the  proper  fric- 
tional  damping.  Figure  57  shows  an  arrange- 
ment which  embodies  these  features  and 
which  has  given  satisfaction. 

While  resistibility  is  easily  defined  as  ability  to  resist  im- 
pressed forces,  a  mathematical  definition  is  impossible,  because 
both  mass  and  friction  share  in  the  resistance.  If  friction  is 
omitted  from  the  discussion,  resistibility  becomes  (in  spindle 
governors)  simply  equivalent  mass  of  governor  at  the  sleeve 
or  collar  of  the  latter,  and,  in  shaft  governors,  equivalent  mo- 
ment of  inertia  of  governor  parts  about  the  suspension  point 
of  the  eccentric.  For  this  reason,  j"y  &™9 
makers  of  direct-acting  governors  J~~ 
should  give  the  equivalent  mass  of 
each  size  of  governor  in  their  cata- 
logues. 

While  it  is  evident  that  valve 
gears  which  impose  great  alter- 
nating or  vibratory  forces  upon  the 
governors  require  the  latter  to  be 
quite  heavy  and  massy,  it  is  less 
evident  how  that  mass  should  be 
distributed  in  the  governors  for  best  advantage.  For  the 
purpose  of  reducing  amplitude '  of  impressed  vibration,  the 
governor  mass  need  not  be  so  arranged  that  all  of  it  pro- 
duces centrifugal  force.  For  reduction  of  cyclical  vibration, 
the  mass  is  very  effective,  if  arranged  as  shown  in  Fig.  58, 
where  both  m:  and  m2  contribute  to  the  resistibility,  whereas 


FIG.  58 


EFFECTS  OF  OUTSIDE  FORCES  85 

mi  only  produces  centrifugal  force.  However,  the  expedient 
of  placing  a  large  part  of  the  governor  mass  outside  of  the 
governor  proper  considerably  reduces  the  promptness  of  the 
latter  and  causes  great  fluctuations  of  the  speed,  whenever  the 
load  changes  suddenly  (see  Chapter  IX).  It  must  not  be  used 
where  close  regulation  is  essential.  In  the  latter  case  it  is  much 
better  either  to  use  a  larger-size  governor,  or  else  to  arrange 
the  additional  mass  in  the  governor  in  such  a  manner  that 
it  furnishes  tangential  inertia  acting  in  the  right  direction  (see 
paragraph  2  of  Chapter  II).  In  that  paragraph  proof  was  fur- 
nished that  the  regulating  force  due  to  tangential  inertia  is 
proportional  to  the  change  of  load  of  the  engine.  Paragraph 
3  of  Chapter  IX  contains  proof  that  tangential  inertia  increases 
the  stability  of  regulation.  As  before  stated,  it  increases 
resistibility  without  increasing  centrifugal  force.  Since  in  a 
vibrating  system  a  comparatively  small  centrifugal  force 
suffices  to  adjust  the  position  of  equilibrium,  tangential  inertia 
furnishes  the  ideal  vibration-resisting  force.  Of  all  types  of 
governors,  shaft  governors  are  subjected  to  greatest  fluctuating 
forces.  The  use  of  tangential  inertia  in  shaft  governors,  which 
was  introduced  by  American  engineers  shortly  after  the 
year  1890,  is,  in  consequence,  well  justified  and  is  correct 
engineering. 

References  to  Bibliography  at  end  of  book:  23,  28,  50. 

2.  Cyclical  Vibrations  of  Governors. —  As  explained  in  the 
preceding  paragraph,  the  necessary  resistibility  of  a  governor 
is  determined  by  the  impressed  force  (resp'y  moment)  and 
by  the  permissible  amplitude  of  the  vibration  of  the  govern- 
or. The  latter  is  determined  chiefly  by  the  consideration 
that,  for  a  constant  load,  the  supply  of  energy  must  be  the 
same,  stroke  after  stroke  of  the  engine.  A  governor  vibrat- 
ing too  much  will  strike  the  stops,  if  the  load  is  either  very 
light  or  very  heavy.  The  result  is  irregular  motion  of  governor 
and  of  engine.  Besides,  vibrations  of  large  amplitude  wear  out 
the  governor  in  short  time,  unless  it  was  specially  designed  for 
such  service. 

Both  requirements,  namely  that  of  clearing  the  stops,  and 


86       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 

that  of  avoiding  wear,  refer  particularly  to  spindle  governors. 
The  latter  are  commonly  so  adjusted  that  their  total  available 
travel  just  varies  the  energy  supply  between  the  limits  of  no 
load  and  full  load,  which  means  that  a  vibrating  governor  strikes 
the  stops  near  the  extreme  ends  of  its  travel:  In  spindle 
governors  a  third  feature  enters,  namely  the  visibility  of  the 
vibration.  Engineers  seem  to  have  an  instinctive  feeling  that 
a  vibrating  governor  is  wrong,  and  take  steps  to  quiet  it. 

Matters  are  very  different  with  shaft  governors.  The 
vibrations  are  not  visible  and,  for  that  reason,  do  not  interfere 
with  any  preconceived  notion  of  operating  engineers.  Experi- 
ence with  vibrating  shaft  governors  has  taught  designers  to 
make  the  supporting  pins  of  liberal  proportions  so  that  wear 
is  slight.  Furthermore,  the  valve  gear  is  frequently  of  such 
nature  that  the  governor  stops  can  be  placed  considerably 
outside  the  limits  of  no  power  and  of  maximum  power.  In 
that  case  the  governor  can  (and  usually  does)  vibrate  with  a 
considerable  amplitude  without  producing  any  harmful  effects 
upon  regulation. 

Evidently,  relatively  greater  vibrations  can  be  permitted 
in  shaft  governors  than  in  spindle  governors,  unless  the  latter 
are  designed  for  cyclical  vibrations.  It  is  also  evident  that  a 
large  number  of  circumstances  influence  the  greatest  permissible 
amplitude  so  that  no  universal  figure  can  be  given  for  that 
quantity.  The  following  values  may,  however,  be  used  as  a 
guide  for  average  conditions: 

For  spindle  governors,  maximum  permissible  amplitude 
equals  ^V  of  governor  travel,  so  that  maximum  displacement 
equals  yV  of  governor  travel. 

For  shaft  governors,  maximum  permissible  angular  ampli- 
tude equals  -jV  of  total  angle,  so  that  maximum  angular  dis- 
placement equals  J  of  total  angle. 

These  are  limiting  values,  and  it  will  pay  in  practice  to 
keep  the  amplitude  of  cyclical  vibrations  somewhat  below  these 
values.  It  should  be  noted  that  the  tendency  of  some  designers 
to  keep  any  and  all  impressed  forces  away  from  governors  for 
the  purpose  of  entirely  eliminating  cyclical  vibrations  is  funda- 
mentally wrong.  In  paragraph  4  of  Chapter  II,  mention  was 


EFFECTS  OF  OUTSIDE  FORCES  87 

made  of  the  fact  that  vibrations  reduce  or  eliminate  friction 
and  the  time  lag  (detention)  caused  by  it.  Consequently, 
moderate  cyclical  vibrations  of  governors  are  beneficial.  Their 
action  in  eliminating  friction  may  be  analyzed  as  follows: 
Let  Q  be  the  regulating  force  which  tends  to  move  the  governor 
collar  at  a  given  instant.  Let  F  be  the  resisting  frictional  force, 
and  let  F  be  greater  than  Q,  so  that  the  governor  would  not 
move,  if  it  were  not  for  the  effect  of  the  impressed  cyclical 
vibration.  Let  f  s  be  the  amplitude  of  the  latter.  While  the 
governor  collar  moves  in  the  direction  of  the  force  Q,  the  latter 
acts  into  the  space  s  and  puts  into  the  governor  the  work  Qs 
in  the  shape  of  kinetic  energy,  so  that  the  governor  moves  its 
center  of  vibration  the  distance  Qs/F  in  the  direction  of  Q. 
During  the  return  travel  against  the  force  Q,  the  latter  reduces 
the  kinetic  energy  of  the  governor  the  amount  Qs  so  that  the 
center  of  vibration  is  again  shifted  the  distance  Qs/F  in  the 
direction  of  the  force  Q.  With  each  complete  vibration,  the 
collar  moves  the  distance  2  Qs/F,  which  means  that  any  force, 
no  matter  how  small,  will  affect  a  vibrating  governor  and  will 
move  it.  Skillful  and  experienced  designers  make  use  of  this  fact. 
The  problem  of  so  selecting  the  resistibility  of  the  governor 
that  the  amplitude  is  kept  within  the  desired  moderate  limits 
consists  of  two  separate  problems,  namely 

(1)  Ascertaining  the  impressed  force  or  moment  as  a  func- 
tion of  time, 

(2)  Double  integration  of  the  resulting   linear  or  angular 
acceleration. 

The  first  part,  namely  the  determination  of  the  impressed 
force  or  moment,  is  really  a  problem  of  engine  or  valve  gear 
design.  The  great  diversity  of  valve  gears  prohibits  a  detailed 
discussion,  so  that  the  latter  must  be  limited  to  a  few  remarks 
concerning  general  guiding  principles. 

Forces  reacting  upon  the  governor  are  caused  by  friction 
of  valves  and  valve  gear  parts,  by  inertia  of  valves  and  valve 
gear  parts,  by  unbalanced  steam  pressure  and  by  unbalanced 
weights  (in  shaft  governors).  In  the  case  of  releasing  gears  the 
principal  force  is  the  friction  between  the  catchblocks  which, 
in  turn,  is  determined  by  the  force  required  to  drive  the  valves. 


GOVERNORS   AND   THE    GOVERNING   OF   PRIME    MOVERS 


, 
the 


This  latter  force  is  found  as  below  given  for  automatic  valve 
gears. 

In  the  case  of  non-releasing  valve  gears  all  inertia  forces 
are  computed  on  the  basis  of  the  valves  being  moved  by  a 
non-vibrating  governor.  To  this  end  the  displacements  of  all 
moving  valves  and  valve  gear  parts  from  their  respective 
midpositions  are  plotted  against  time.  The  second  derivatives 
of  these  curves  furnish  the  accelerations  which  later,  upon 
multiplication  by  the  respective  moving  masses,  furnish  the 
inertia  forces.  Forces  caused  by  friction  of  valves  and  by  un- 

balanced  steam 
pressure  on  valve 

Stems     are     COm- 

Curve  of  impressed  ,      ., 

Moment  (also  of  puted    from 

Angular  Acceleration.)  well  known 

of  mechanics. 

In  Fig.  59  the 
upper  curve  is  an 
example  of  an  im- 
pressed moment 
plotted  against 
time  (one  revolu- 
tion  of  the 
engine).  The 
curve  should  not 
be  taken  as  repre- 
senting all  pos- 
sible cases.  On  the  contrary,  curves  of  impressed  moments  are 
most  varied  in  shape  and  depend  very  much  upon  the  type  of 
valve  gear. 

From  the  moment  curve  the  amplitude  is  found  by  a  double 
integration.  If  the  impressed  moments  are  divided  by  the 
moment  of  inertia  of  the  governor  parts,1  the  moment  curve 

1  For  the  governor,  Fig.  8,  the  moment  of  inertia  is  with  sufficient  accuracy  mass 
(4)  times  If  plus  mass  (5)  times  l£  plus  moment  of  inertia  of  connecting  link.  For 
a  governor  of  the  type  of  Fig.  9  both  impressed  moment  and  moment  of  inertia 
must  be  referred  to  either  point  (4)  or  else  to  point  (5).  If  (4)  is  made  the  point  of 

reference,  the  moment  of  inertia  is  roughly  J  =  m\  If 


\ 


Curve  of  Angular 
Velocity  of 
Vibration. 


Curve  of  Angular 
Displacement. 


FIG.  59 


EFFECTS  OF  OUTSIDE  FORCES 


89 


becomes  a  curve  of  angular  accelerations  which,  upon  being 
integrated  once  furnishes  angular  velocity  of  vibration.  The 
second  integration  furnishes  angular  displacement.  Each 
integration  can  be  carried  out  either  by  the  addition  of  mean 
ordinates,  or  by  the  use  of  a  planimeter.  Or  else  the  double 
integration  may  be  accomplished  in  one  operation  by  the 
drawing  of  an  equilibrium  polygon.  It  is  evident  that  in  a 
cyclical  vibration  the  mean  value  of  the  angular  velocity  of 
vibration  must  be  zero  and  that  likewise  the  mean  value  of 
the  impressed  moment  must  vanish.  This  fact  must  be  observed 
in  the  integration.  In  the  foregoing  the  influence  of  friction 
has  been  neglected.  Reasons  for  the  advisability  of  neglecting 
it  were  given  in  paragraph  1  of  the  present  chapter. 

For  a  fairly  complete  solution  the  whole  calculation  should 
be  made  for  at  least  three  positions  or  configurations  of  the 
governor.  While  the  work 
is  not  difficult,  it  is  certainly 
long  and  tedious  so  that  a 
healthy  guess  is  usually  con- 
sidered the  lesser  evil. 

A  great  deal  of  trouble 
has  been  caused  by  cyclical 
vibrations  due  to  unbalanced 
weights  in  shaft  governors. 
Although  this  type  of  govern- 
or has  not  the  importance 


to-day  which  it  had  at  the 
end  of  the  nineteenth  cen- 
tury, a  brief  discussion  of  the  underlying  principles  will  even 
at  this  date  be  helpful  to  a  large  number  of  engineers. 

Figure  60  diagrammatically  represents  a  shaft  governor 
with  an  unbalanced  weight  such  as  is  used  for  instance  in  the 
Rites  governor.  (1)  is  the  center  of  the  shaft.  (2)  is  the  sus- 
pension point  of  weight  W  whose  mass  center  is  (3).  The  sys- 
tem rotates  about  (1)  with  uniform  angular  velocity  u.  Spring 
(4)  is  so  dimensioned  that  it  balances  the  centrifugal  force  of 
W  in  any  position. 

The  motion  of  weight  W  can  be  found  under  the  following 
simplifying  assumptions  : 


FIG.  60 


90     GOVERNORS    AND    THE  GOVERNING    OF    PRIME    MOVERS 

(1)  The  angular  displacement  of  the  weight  is  so   small 
that  it  can  be  neglected  compared  to  the  average  value  of 
u  t  which,  of  course,  is  45°. 

(2)  Effects  of  friction  and  of  resonance  are  neglected.    Jus- 
tification for  these  simplifications  is  given  in  paragraph  1. 

The  angular  acceleration  of  the  weight  W  (the  moment  of 
inertia  'of  which  about  point   (2)  is  J)  is 

d2i       du               W  L  sin  u  t 
=  a  = 


dP       dt 

By  integrating  l  twice  we  obtain  first 

Du  =  —  — —  cos  ut+K 
uJ 

and  then 

W  L 
Di  =  -  —7-  sin  u  t  +  K  t  +  K', 

u-  J 

where  K  and  K'  are  constants  the  values  of  which  depend  upon 
the  location  of  the  zero  line  as  shown  in  Fig.  59.  Du  is  the 
change  in  angular  velocity,  or  the  difference  of  angular  velocity 
between  weight  W  and  shaft  (1),  or,  in  other  words,  the  rela- 
tive angular  velocity  of  weight  W.  For  a  cyclical  vibration 
the  average  value  of  Du  must  vanish,  and  to  have  that  occur, 
K  must  equal  zero.  The  same  reasoning  holds  true  for  Di 
and  Kf,  so  that  the  angular  displacement  of  vibration  becomes 

W  L  W  L 

Di  =  —  -y~r  sin  u  t  with  angular  amplitude  of  ±    2  , (1) 

u  J  U"  J 

Equation  (1)  teaches  that  Di  reaches  a  maximum  (negatively), 
when  sin  u  t  becomes  a  maximum  which  occurs  in  point  (5)  of 
Fig.  60.  In  points  (6)  and  (7)  sin  u  t  =  0  so  that  there  is  no 
displacement.  The  effect  of  gravity  in  this  simple  case  then 
consists  in  lifting  the  center  of  the  (slightly  distorted)  circle, 

W  L2 

which  the  weight  describes,  the  distance     2     .      If    H    is    the 

u  J 

radius  of  gyration  of  the  weight  W,  the  distance  which  the 

1  For  the  benefit  of  those  who  are  not  versed  in  integration,  it  has  been  done 
graphically  in  the  Appendix,  Fig.  139. 


EFFECTS  OF  OUTSIDE  FORCES  91 

m  g  L2        (j  L2 

weight  is  raised  becomes  — ; —  =  '     The   center  of  the 

u2  m  H2      u2  H2 

circle  described  by  the  eccentric  which  is  linked  to  the  weight 
W  is  likewise  shifted.  The  direction  of  the  displacement  de- 
pends upon  the  kinematic  connection.  Early  experimenters 
were  surprised  to  find  the  raising  of  the  path  of  the  vibrating 
weight;  but  this  fact  appears  quite  simple  and  natural,  if 
comparison  is  made  with  the  ordinary  pendulum,  in  which  the 


FIG.  61 

average  location  of  the  mass  center  is  higher  during  vibration 
than  it  is  when  the  pendulum  is  at  rest. 

Other  experimenters  doubted  the  raising  of  the  center  of 
the  path,  because  they  had  found  a  shifting  to  one  side.  Again 
the  explanation  is  not  difficult.  From  the  theory  of  vibrations 
it  is  known  that  friction  causes  a  phase  lag  which,  in  the  case 
of  resonance,  reaches  the  value  of  90°.  Evidently,  the  actual 
direction  of  the  displacement  varies  with  the  friction  so  that 


92     GOVERNORS    AND    THE    GOVERNING    OF    PRIME    MOVERS 

it  is  advisable  not  to  count  upon  any  given  direction,  but  rather 
to  keep  the  amplitude  of  vibration  within  safe  limits  as  pre- 
viously given  in  this  paragraph.  For  a  given  angular  velocity 
u  of  the  governor  shaft  the  displacement  may  be  kept  small 

by  making  radius  of  gyra- 
tion H  large  compared  to 
mass  radius  L .  For  small 
values  of  u,  say  for  less 
than  150  revolutions  per 
minute,  the  requirement 
of  small  amplitude  means 
(with  a  single  centrifugal  weight,  as  in  Fig.  60)  so  small  a  value 
of  L  that  the  centrifugal  moment  becomes  insufficient  for  speed 
counting.  The  use  of  a  single  weight  is,  therefore,  inadvisable 
for  slow  speeds,  and  double  weights,  partly  or  wholly  balancing 
each  other,  must  be  used. 


FIG.  62 


FIG.  63 

An  actual  case  from  the  author's  practice  will  serve  to  illus- 
trate these  theories.  The  Rites  shaft  governor  shown  in  Fig. 
61  was  originally  built  with  a  single  annular  weight  W\.  The 
suspension  point  of  the  latter  is  at  (2) ;  its  mass  center  is  at  (3) . 
The  center  of  the  eccentric  swinging  rigidly  with  weight  W\  is 
at  (8).  The  governor  was  noisy,  making  a  hammering  sound. 


EFFECTS   OF   OUTSIDE   FORCES 


93 


Indicator  cards  taken  from  the  engine  had  the  shape  given  in 
Fig.  62.     A  pencil  point  fastened  to  the  eccentric  rod  close  to 


FIG.  64 

the  governor  described  the  egg-shaped  curves  reproduced  in 
Fig.  63.  The  outer  curve  is  described  with  full  load  on  the 
engine.  The  spring  holds  the  governor  against  the  stop  most 
of  the  time  so  that  the 
motion  of  the  eccentric  is 
almost  symmetrical.  The 
inner  curve  is  described 
with  a  partial  load  on  the 
engine.  It  is  shifted  both 
upward  and  sideways.  To 
remedy  matters,  the  weight 
T72  with  suspension  point 
(6)  and  mass  center  (7)  was 
added,  and  was  connected 
to  Wi  by  a  link.  The  two 
weights  now  almost  balance 

each  other  against  gravity.  The  results  were  very  satisfactory. 
Figure  64  shows  the  curves  described  by  the  same  point  on  the 
eccentric  rod  after  the  change,  and  Fig.  65  shows  the  correspond- 
ing indicator  cards.  The  hammering  of  the  weights  in  the 


94       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 

governor  had  entirely  disappeared.  Of  course,  a  new  and 
stronger  spring  (4)  was  installed,  because  the  addition  of  the 
second  weight  Wi  increased  the  centrifugal  moment  for  the 
desired  speed. 

Cyclical  vibrations  of  governors  are  also  caused  by  the 
interaction  of  governor  and  prime  mover.  Their  period  differs 
from  that  of  the  vibrations  studied  in  the  present  paragraph. 
They  are  dealt  with  in  Chapter  IX. 

References  to  Bibliography  at  end  of  book:  28,  40,  60,  59,  63,  70. 


CHAPTER   IX 


INTERACTION   BETWEEN   DIRECT-CONTROL  GOVERNOR 
AND  PRIME  MOVER 

1.  Action  of  Governors  Regulating  Prime  Movers.  —  In 
paragraph  1  of  Chapter  I  the  statement  was  made  that  govern- 
ors are  used  to  keep  some  one  quantity  practically  con- 
stant while  the  output  of  a  prime  mover  varies.  The  purpose 
of  the  following  investigations  is  to  find  out  to  what  extent 
the  aim  of  keeping  angular  velocity  practically  constant  has 
been  realized. 

In  Fig.  66  load  or  output  has  been  plotted  against  time,  and 
two  changes  of  load  have  been  indicated,  one,  (1)(2),  sudden, 
and  the  other,  (3)  (4), 
gradual.  In  an  ideal 
regulation  the  gover- 
nor would  follow  the 
change  of  load  with- 
out time  lag.  In  that 
ideal  case  the  broken 
line  (/)(*)  (3)  (4) 
would  also  represent 
governor  position. 

In  reality,  governors  have  mass  which  requires  time  for  its 
acceleration,  so  that  a  time  lag  exists  between  load  and  governor 
position.  During  the  interval  of  lack  of  coincidence  between 
load  (power  consumed)  and  power  generated,  the  difference  of 
work  causes  a  rise  or  fall  of  speed  which,  in  turn,  affects  the 
motion  of  the  governor. 

In  the  language  of  mechanics,  the  governor  and  the  prime 
mover  form  a  system  with  two  degrees  of  freedom.  Translated 
into  everyday  language  it  means  that  the  position  of  the 
governor  determines  the  rate  at  which  the  speed  of  the  prime 
mover  varies,  and  that  the  speed  of  the  prime  mover  determines 

95 


LOAD 
(Ideal 
Governor 
Position") 

-  NO  Load 
( 

P                       © 

<D                  ^^~ 

.  Full  Load 

3F 

rime 
FIG.  66 

96       GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


Governor 

Position 

and 

Load 


Old  Position 


New  Position 


Change  of  Load 


Time 
FIG.  67 


the  force  which  tends  to  change  the  position  of  the  governor. 
To  every  load  on  the  prime  mover  there  belongs  a  certain 
position  of  the  governor,  and  to  every  position  of  the  governor 
belongs  a  certain  speed,  but  these  two  variables  --  (1)  governor 

position,  (2)  speed  of 
prime  mover — are  free 
to  vibrate  about  their 
equilibrium  values. 

In  the  motion  result- 
ing from  a  change  of 
load  a  broad  distinction 
must  be  made  between 
the  two  following  cases: 

(1)  Following  a  disturbance  of  equilibrium  the  governor 
reaches  its  new  position  of  equilibrium  after  a  finite  number 
of  vibrations  the  amplitude  of  which  continually  decreases  (see 
Fig.  67). 

(2)  The  governor  performs  vibrations  with  ever  increasing 
amplitude  about  its  new  position  of  equilibrium  and   never 
comes  to  rest  (Fig.  68). 

Case  No.  2  is,  of  course,  worthless;  case  No.  1  is  the  only 
allowable  one  in  practice.  Guarantees  for  closeness  of  regula- 
tion usually  state  that  for  a  given  and  sudden  change  of  load 
the  maximum  speed 
variation  shall  not 
exceed  a  certain 

amount.        Any    SUCh     Governor 

guarantee  really  in-    Position 
volves  two  promises, 
namely  : 

(a)  that  the  regu- 
lation shall  be  stable, 

(b)  that  the  amplitude  of  the  first  wave  shall  be  small. 

In  accordance  herewith  the  problem  of  regulation  divides 
itself  into  two  problems,  to  wit 

(a)  the  investigation  of  the  stability  of  regulation, 

(b)  computation  of  the  greatest  speed  variation. 

These  two  problems  form  the  subject  of  the  following  para- 
graphs. 


and 
Load 


-   Time 
FIG.  68 


Governor 
Position 
and 

Load 

Old  Position  of 

S~\            f*\ 

/             \     New  Position    \of 

/                  \         Equilibrium 

Equilibria  fn 

Time 
FIG.  69 


INTERACTION   BETWEEN   GOVERNOR   AND  PRIME   MOVER       97 

Between  the  conditions  of  stability  (Fig.  67)  and  of  insta- 
bility (Fig.  68)  lies  the  limiting  case  (Fig.  69).  In  this  limiting 
case  any  change  of  load  releases  a  vibration  which  continually 
maintains  its  original  amplitude.  The  regulation  is  neither 
stable  nor  unstable.  The  limiting  case  is,  naturally,  never 
met  with  in  practice,  except  accidentally,  but  it  marks  the 
division  line  between 
useful  and  useless, 
and  is  therefore  of 
importance.  In  ad- 
dition, it  has  the 
advantage  of  being 
amenable  to  mathe- 
matical investigation 
by  comparatively  simple  means.  The  condition  of  stability 
will  turn  out  to  be  independent  of  the  relative  load  change. 
Hence,  stability  at  any  change  of  load  includes  the  case  of 
constant  load.  If  the  regulation  is  stable,  the  governor  will 
not  hunt  at  constant  load. 

To  make  an  analytical  solution  possible,  simplifying  assump- 
tions must  be  made.  The  various  existing  theories  differ 
mainly  in  the  nature  of  these  assumptions.  Among  the  theories 
thus  offered,  the  one  put  forth  by  Professor  Stodola  in  1899 
appears  to  the  author  to  contain  the  smallest  departure  from 
actual  conditions.  Besides,  all  the  assumptions  made  by  Sto- 
dola are  of  such  nature  that  the  effect  of  the  neglect  can  be 
estimated.  The  following  principal  assumptions  will  be  made: 

(1)  There  is  no  time  lag  between  the  position  of  the  governor 
(including  torque-controlling  mechanism)  and  the  torque  cor- 
responding to  the  governor  position.     In  the  language  of  Mr. 
Hartnell   (Inst.  of  Mech.  Engineers,  1882),  there  is  no  deten- 
tion due  to  stored-up  energy  between  the  regulating  device 
and  the  prime  mover.1 

(2)  The  action  of  the  governor  is  continuous.     While  this 
is  no  assumption  with  steam  and  water  turbines,  it  is  a  simpli- 
fying assumption  for  steam  and  gas  engines,  where  the  governor 


1  This  excludes  from  the  following  derivations  the  case  of  the  compound  engine 
with  large  receivers  or  the  case  of  compound  steam  turbines  with  large  receivers. 


98      GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

action  is  intermittent  from  stroke  to  stroke.  This  simplifica- 
tion is  well  permissible,  because  the  time  in  which  a  governor 
finally  assumes  its  new  position  after  a  change  of  load  always 
extends  over  a  great  number  of  engine  revolutions  (see  Fig.  70) . 
For  minor  assumptions  see  the  following  paragraphs. 

References  to  Bibliography  at  end  of  book :  36,  73. 

2.  Limiting  Case.  —  In  order  that  we  may  proceed  from 
the  simple  to  the  more  complex,  the  following  minor  assump- 
tions will  be  made  in  this  paragraph: 

(1)  The  governor  is  free  from  friction. 

(2)  The  governor  is  so  large  that  the  frictional  resistance  of 
the  valve  gear  can  be  neglected. 

(3)  The  radial  displacement  of  the  centrifugal  weights  (mo- 
tion of  representative  point)  is  so  small  that  the  centrifugal 
force  may  be  considered  constant  over  the  range  of  motion. 

Changes  7/me 


F=? 


•  One  Revolution  of  Engine 
FIG.  70 

(4)  The  torque  exerted  by  the  prime  mover  is  proportional 
to  the  displacement  of  the  governor  from  no-load  position. 

The  actions  which  take  place  after  a  change  of  load  has 
occurred  are  illustrated  by  Fig.  71.  The  abscissae  show  "  posi- 
tion of  representative  point  "  which  in  this  paragraph  means 
"radial  distance  of  mass  center  of  centrifugal  weights  from 
center_qf  rotation."  All  forces  and  accelerations  are  to  be 
referred  to  this  point  and  to  radial  motion,  as  was  explained  in 
earlier  paragraphs.  Instead  of  this  motion,  that  of  the  sleeve 
or  collar  may  be  used  with  spindle  governors,  but  the  selected 
motion  is  applicable  to  spindle  governors  and  to  shaft  governors, 
whereas  the  apparently  simpler  and  more  easily  observed  mo- 
tion of  the  sleeve  cannot  be  used  with  shaft  governors.  The 
relation  of  the  diagram  (Fig.  71)  to  the  governor  proper  is 
illustrated  by  Fig.  72.  The  meaning  of  the  various  ordinates 
of  Fig.  71  will  become  clear  from  the  following  reasoning: 


INTERACTION  BETWEEN   GOVERNOR  AND   PRIME   MOVER       99 

Let  a  prime  mover  develop   the   balanced   torque    (1)(2) 
and   let  the  load  be  suddenly   reduced   to   a   torque    (4)  (5), 


of  Representative  Point 


Velocity  of  represemat 
/point  for  damped  go 


Velocity  of  representative 
point  forfrictionless 
governor. 


(g)          x^Acoswt 


FIG.  71 


then  the  torque  (2)  (3)  becomes  unbalanced  and  produces  an 
angular  acceleration  equal  to 

unbalanced  torque  M0  A 

moment  of  inertia  of  rotating  masses  of  prime  mover      /   AQ 


100     GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


where  A/AQ  —  relative  change  of  load.  The  change  of  velocity 
resulting  from  this  acceleration  sets  the  governor  in  motion, 
slowly  at  first,  because  the  governor  mass  must  be  accelerated 
from  rest.  This  motion  of  the  governor  and  of  the  torque- 
controlling  mechanism  reduces  the  unbalanced  torque  and  the 
acceleration.  Let  at  a  certain  time  the  governor  point  be  x 

*-=  2 /amplitude  of  vibration 

-Diagram  of  regulatin0  forces  and  velocities 
•Motion  of  representative  point 
f^^^r— Rotating  auxiliary  vector 


FIG.  72 


distant  from  its  new  position  of  equilibrium;   then  the  angular 
acceleration  of  the  prime  mover  is 

•M      Mo    x 


the  angular  acceleration  of  the  governor  is  proportional  to  a 
and  depends  upon  the  ratio  of  gearing  between  prime  mover 
and  governor.  While  the  governor  moves  towards  (4),  its  new 
position  of  equilibrium,  a  is  positive  and  the  angular  velocity 
of  the  prime  mover  increases,  until  point  (4)  has  been  passed. 
The  accelerating  forces  acting  upon  the  governor  are  dis- 


INTERACTION  BETWEEN  GOVEn^Q^Plfm     101 


closed  by  the  middle  diagram  of  Fig.  71.  Line  (14)  (10)  (9) 
represents  the  curve  of  equilibrium  speeds  (angular  velocities) 
of  the  governor,  or,  to  another  scale,  the  corresponding  speeds 
of  the  prime  mover.  The  base  line  for  this  curve  lies  down 
beyond  the  limits  of  the  page.  As  the  governor  moves  from 
point  (1),  its  old  position  of  equilibrium,  towards  (4),  the  speed 
of  the  system  grows.  Compare  also  Fig.  87.  Let  the  rise  of 
speed  be  indicated  by  the  curve  (11)  (7)  (18).  Since  for  posi- 
tion x,  (6)  indicates  the  equilibrium  speed,  and  (7)  indicates  the 
actual  speed,  the  excess  speed  (6)  (7)  causes  an  unbalanced  cen- 

/.--..,.  ,  •  ,    •  .      4|  ,.  („„  excess  (6)  (7 

tnfugal  force  which  is  approximately  equal  to!  2C 

~~~^~*3*—^^~  ^\       ^^-—  1  . 

(see  equation  3,  ol  paragraph  1,  Chapter  II).  UnTess~this  Torce 
is  counteracted  by  some  resistance  (and  it  is  at  present  assumed 
that  there  is  no  resisting  friction  or  oil  gag  pot),  it  will  ac- 
celerate the  governor  (representative  point)  until  point  (9)  has 
been  reached,  that  is  when  actual  speed  and  equilibrium  speed 
coincide.  But  the  limiting  case  —  now  under  discussion  — 
of  never  ending  vibrations  of  constant  amplitude  requires  that 
the  amplitudes  on  both  sides  of  the  position  of  equilibrium  — 
(10)  or  (4)  (5)  —  must  be  equal.  Since  the  accelerating  un- 
balanced forces  are  approximately  proportional  to  the  excess 
speeds,  the  vertically  section  lined  area  (14)  (11)  (7)  (18)  (9)  (10) 
represents  ^o  some  scale  the  kinetic  energy  stored  up  in 
the  governor,  when  it  reaches  point  (9)]  with  conditions  as 
depicted  here  the  governor  cannot  possibly  come  to  rest  at 
(13),  but  will  come  to  a  temporary  stop  farther  away  from  the 
position  of  equilibrium  than  the  starting  point  is.  This  fact  is 
evident  from  a  study  of  the  curve  of  velocity  of  the  representa- 
tive point  at  the  foot  of  Fig.  71.  *  Regulation  by  a  governor 
devoid  of  friction  is  therefore  impossible.  This  theorem  was 
first  deduced  by  Wischnegradsky  in  1877.  Whether  the  or- 
dinates  of  the  curve  (11)  (7)  (18)  (9)  are  right  or  not  does 
not  matter;  for  if  the  actual  curve  were  not  (11)  (7)  (18)  (.9), 

1  The  over-traveling  of  the  governor  is  caused  solely  by  the  inertia  of  its  masses. 
If  centrifugal  force  could  be  produced  without  mass,  the  present  paragraph  would 
be  superfluous.  The  harmful  effects  of  mass  can  be  practically  eliminated  in  relay 
governors.  See  the  paragraph  on  that  subject. 


102    GOYfcHSOES^NE) -THE:.  GOVERNING  OF  PRIME  MOVERS 

but  the  dotted  curve  lying  below  it,  the  governor  would  shoot 
past  the  mark  just  the  same,  and  the  amplitude  of  the  vibra- 
tions would  increase  without  limits. 

In  order  to  prevent  this  undesirable  action,  and  in  order 
to  bring  about  the  constant  amplitude  vibrations  of  the  limiting 
case,  we  must  modify  the  forces  acting  upon  the  governor  by 
other  forces  in  such  a  manner  that  the  kinetic  energy  stored 
up  on  the  way  from  (11)  to  (10),  or  from  (1)  to  (4),  is  recon- 
verted into  potential  energy  at  point  (13).  Just  what  must 
be  done  to  this  end  is  easily  seen,  if  the  excess  speed  (6)  (7) 
is  resolved  into  two  component  parts  (6)  (8)  and  (7)  (8).  The 
two  component  parts  are  quite  different  in  their  action.  The 
part  (6)  (8)  becomes  a  retarding  force  after  the  new  position 
of  equilibrium  —  point  (10)  —  has  been  passed,  whereas  the 
component  (7)  (8)  remains  an  accelerating  force  all  the  time. 
The  forces  resulting  from  these  excess  speeds  have  received 
various  names.  The  force  resulting  from  (6)  (8)  has  been 
named  "  static  regulating' force"  or  " regulating  force  due  to 
wrong  position,"  while  the  force  due  to  (7)  (8)  has  been  called 
" dynamic  regulating  force"  or  " regulating  force  due  to  wrong 
speed."  In  this  book  the  terms  " static"  and  "dynamic  regu- 
lating force  "  are  used. 

The  areas  (11)  (H)  (10)  and  (10)  (15)  (13)  are  equal,  which 
means  that  any  kinetic  energy  which  has  been  stored  up 
in  the  governor  parts  while  traveling  from  (11)  to  (10)  is 
reconverted  into  potential  energy  on  the  way  from  (10)  to  (13), 
provided  that  the  static  regulating  force  alone  acts,  which 
means  that  the  dynamic  regulating  force  must  not  be  allowed 
to  act. 

To  this  end  the  latter  force  must  always  be  balanced  by 
some  external  resistance,  for  instance  solid  or  liquid  friction; 
and  the  question  arises:  Can  a  resisting  force  be  found  of  such 
a  nature  that  it  will  always  just  equal  the  dynamic  regulating 
force,  and  oppose  it?  In  attempting  to  answer  this  question 
we  must  remember  that  a  force  diagram  as  represented  by  the 
straight  line  (14)  (15)  results  in  a  harmonic  vibration.  From 
mechanics  it  is  known  that  in  harmonic  vibration  the  diagram 
of  velocities  of  the  vibrating  body,  plotted  against  its  position, 


INTERACTION   BETWEEN   GOVERNOR  AND  PRIME   MOVER     103 

is  either  a  circle  or  an  ellipse,  depending  upon  the  scale  of  the 
ordinates.  Such  a  diagram  of  velocities  is  shown  at  the  bot- 
tom of  Fig.  71.  But  if  the  motion  of  the  governor  point  is 
harmonic,  the  curve  (1 1}  (7)  (1 8)  (9)  is  also  an  ellipse,  as  will 
be  proved  further  down.  The  velocity  of  the  governor  point 
is,  therefore,  always  proportional  to  the  instantaneous  value 
of  the  dynamic  excess  speed;  and  since  the  force  caused  by  the 
latter  is  to  be  counteracted,  the  counteracting  force  must  be 
proportional  to  the  linear  speed  of  vibration  of  the  governor  point. 

An  oil  gag  pot  comes  very  close  to  furnishing  such  a  resisting 
force.  Its  resistance  grows  with  some  power  of  the  velocity, 
and  for  the  slow  motion  of  a  governor  the  resistance  is  very 
nearly  proportional  to  the  velocity  itself.  As  a  rule,  the  re- 
sistance offered  by  a  gag  pot  is  adjustable.  Let  it  be  so  adjusted 
that  the  resistance  just  equals  the  dynamic  regulating  forces 
caused  by  the  excess  speeds,  such  as  (7)  (8).  Then  all  con- 
ditions are  fulfilled  for  the  occurrence  of  the  "  limiting  case." 
Discussion  of  the  importance  of  this  case  is  profitably  post- 
poned, until  the  greatest  speed  fluctuation  (18)  (19)  =  2  ue 
has  been  calculated,  which  will  now  be  done. 

With  the  dynamic  regulating  forces  always  balanced  by 
the  oil  pot,  the  forces  represented  by  line  (14)  (15)  produce 
harmonic  vibrations  absolutely  identical  with  those  treated  in 
Chapter  VII.  Their^quation  is  x  =  A^o^w  t,  where  A  is  the 
amplitude  (see  Fig.  71,  bottom)7~and  w  is  the  angular  velocity 
of  the  auxiliary  vector  (see  Fig.  72).  The  latter  (viz.  w)  and 
the  time  of  natural  vibration  of  the  governor  are  interconnected 

by  the  equation  w  =  —•    substituting  for  Tn  from   equation 

J-  n 

(I)  Chapter  VII,  we  obtain 


w=  vC y^i_L (2) 

TT      2me(r0  -  ri) 

In  this  equation  the  letters  have  the  same  meaning  as  before, 
namely 

p    =  static  fluctuation,  found  from  tangent  to  characteristic, 
C    =  average  centrifugal  force, 


104    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

AQ  =  radial  travel  of  weights  (see  Fig.  71), 

me  =  equivalent  mass,  including  all  valve  gear  parts  moving 

with  the  governor  (see  Chapter  VII). 

Tn  (resp.  w)  determines  the  time  during  which  the  un- 
balanced moments  M,  top  of  Fig.  71,  can  act  to  vary  the  velocity 
u  of  the  prime  mover.  The  law  which  this  variation  of  u  fol- 
lows is  found  in  the  following  manner:  The  angular  accelera- 
tion of  the  prime  mover  is  (equation  No.  1,  page  100) 

MQ     X          A    MQ 

a  =  —=-  —  cos  wt. 

I       AQ  AQ       I 

But  the  change  of  angular  velocity  in  the  time  t  is 
Du  =    I  a  dt  =  -  I  cos  wt  d(wt) 

J  AQ      I  W  J 

=  -      ~ —  (difference  of  sin  wt) (3) 

An     1  W 


If    we    start    with  t  =  0    at    the    vertical    (2)(3)(1)(11),  the 
initial  value  of  sin  w  t  is  0  and  we  have 

A  MQ 
Du  =  —  - —  sin  wt. 

AQ   I  W 

Forming  the  expression  sin2  wt  +  cos2  wt  =  1,  we  obtain 


A_    Mo\2       A2 

AQ       I  W 


which  is  the  equation  of  an  ellipse.  This  is  the  proof  for  the 
elliptic  shape  of  the  curve  (11)  (7)  (18)  (9),  promised  on 
page  103. 

The  maximum  value  for  Du,  namely  ue  =  (10)  (18)  follows 

by  substitution  of  -  for  w  t.     Hence 


____        _ 

AQ    IW  A0       I        *    2    p    C" 

Equation  (4)  furnishes  the  magnitude  of  the  never-ending 
speed  fluctuation  of  the  limiting  case.  In  the  discussion  of 
this  case  the  following  statements  will  be  taken  up: 


INTERACTION   BETWEEN   GOVERNOR  AND   PRIME   MOVER     105 


(1)  Stability  of  regulation  can  always  be  enforced  by  an 
oil  pot,  provided  that  p  is  positive. 

(2)  The  speed  fluctuation  given  by  equation    (4)   is  the 
smallest   fluctuation   possible   for   a   given   sudden   change   of 
load. 

(3)  Stability    of    regulation    and    smallest    possible    speed 
fluctuation  depend  in  part  only  upon  the  properties  of  the 
governor.    A  large  part  of  the  responsibility  for  correct  regula- 
tion rests  with  the  prime  mover. 

The  correctness  of  statement  No.  1  is  practically  self- 
evident  from  the  reasoning  followed  in  the  present  chapter, 
and  becomes  very  clear  from  the  fact  that  the  dynamic  regu- 
lating force  (7)  (8)  of  Fig.  71  and  73,  no  matter  how  great, 
can -always  be  balanced  by 
an  oil  gag  pot.  However, 
it  may  also  be  deduced 
mathematically  from  equa- 
tion (4)  by  the  relation  that 
regulation  is  stable  as  long 
as  ue  is  not  imaginary. 
Now,  the  only  quantity 
under  the  radical  which  can 
become  negative  is  the 
static  fluctuation  p.  All 
other  quantities  are  neces- 
sarily positive.  Accordingly,  the  radical  can  never  become 
imaginary  as  long  as  p  is  positive. 

It  should,  however,  be  thoroughly  understood  that  an  oil 
pot,  while  producing  stability  of  regulation,  does  not  prevent 
changes  of  speed;  when  the  load  changes,  it  can  only  keep 
them  within  limits,  the  extent  of  which  is  given  in  equation  (4). 

For  proof  of  statement  2  refer  to  Fig.  73.  It  will  be  remem- 
bered that  the  ellipse  '(11)  (7)  (18)  represents  not  only  the 
speed  changes,  but  also  the  oil  pot  forces  of  the  limiting  case; 
from  that  it  follows  that  damping  the  vibrations  out  of  existence 
requires  a  tightening  of  the  oil  brake.  But  the  latter  action 
retards  the  motion  of  the  governor  still  more.  The  speed  must 
vary  correspondingly  more  for  the  first  wave,  so  that  (10)  (21) 


106    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

is  greater  than  (10)  (18).  If,  on  the  other  hand,  the  oil  pot 
forces  are  reduced  below  the  value  required  for  the  limiting 
case,  the  speed  fluctuation  of  the  first  wave  is  reduced,  true 
enough,  but  the  amplitudes  of  the  governor  vibration  and  with 
them  the  speed  fluctuations  continually  increase,  so  that  after  a 
few  waves  they  exceed  ue  of  the  limiting  case. 

While  the  speed  fluctuation  of  a  practical  case  of  stable 
regulation  (for  instance  (10)  (21)  )  can  be  computed  numerically, 
the  general  solution  for  this  fluctuation  presents  almost  insur- 
mountable difficulties.  And  since  even  the  numerical  calcu- 
lation of  an  individual  case  involves  exponential  functions,  the 
use  of  equation  (4),  giving  the  minimum  possible  fluctuation, 
recommends  itself  on  account  of  its  simplicity. 

For  proof  of  statement  No.  3,  equation  (4)  will  be  trans- 
formed as  follows  : 


ue      I  A  e 

-7—  V--TT--  V-  ..........  (4a) 

u        2  AQ  1  u  C  p 

Ue 

The  fraction  —  equals  the  relative  speed  fluctuation. 
u 

It  can  easily  be  shown  that  the  factors  -  ~^~~r~  depend 

£  .Ao  1  U 

upon  circumstances  over  which  the  governor  has  no  control. 
^ 

For  —  is  that  fraction  of   the  total   capacity  of  the  prime 
•o-o 

mover  which  is  suddenly  put  on  or  removed.    For  the  develop- 

ing of  complete  sine  harmonic  vibrations  the  upper  limit  of 

^| 

this  fraction  is  J.    If  values   of  —  between  £  and  1   are   COn- 

AQ 

sidered,  the  total  speed  fluctuation  (18)  (19)  of  Fig.  71  cannot 
develop,  but  equation  (4)  may  still  be  used  as  an  approximation 
for  finding  the  fluctuation  (10)  (18)  of  the  first  wave.  Evi- 
dently the  speed  fluctuation  is  proportional  to  the  fraction  of 
total  load  suddenly  removed  or  applied. 

The  factor  -  —  is  of  particular  interest.     It  has  a  physical 
meaning  which  is  revealed  by  a  test  for  dimensions.    Substitu- 


INTERACTION  BETWEEN  GOVERNOR  AND  PRIME   MOVER     107 

tion   of   dimensions   for   moment,   moment   of  inertia   and   of 
angular  velocity  furnishes 

length  X  force  1 


force  1         time 

X  time2  X  length2  X 


length  '  N  time 

I  u 
Hence  —  is  a  special  time.     From  the  equation 

JVJ.    o 

unbalanced  moment  X  time  = 

moment  of  inertia  X  change  of  angular  velocity, 

I  u 
it  follows  that  -   -  is  that  time  in  which  the  maximum  torque  l 

MQ 

MQ  of  the  prime  mover  accelerates  the  rotating  masses  of  the 
latter  from  rest  to  their  regular  velocity  u.  Professor  Stodola 
gave  it  the  name  "starting  time.'7  Hereafter  it  will  be  denoted 

1  1  I  u       -  I  u2 

by   T8.    The  additional  relation  -T8  =  -  -77-   =  2—-     shows 

Z  Z   MQ  MQ  U 

that  J  Ts  is  the  ratio  of  kinetic  energy  stored  up  in  the  revolving 
masses  at  normal  speed  to  the  maximum  power  of  the  prime 

mover.     T8  =  -ij-  then  depends  solely  upon  the  kinetic  energy 

MQ 

stored  up  in  the  revolving  masses  (flywheels,  turbine  disks, 
etc.)  per  unit  of  capacity  of  the  prime  mover,  and  the  smallest 
possible  speed  fluctuation  depends  directly  upon  this  quantity. 
This  very  important  fact  has  been  too  often  overlooked  —  and 
is  still  being  overlooked  —  by  builders  of  engines  and  turbines 
who  design  or  buy  governors  solely  upon  the  basis  of  static 
fluctuation  and  who  later  on  wonder  why  the  actually  occurring 
speed  fluctuation  is  "so  much  greater  than  it  should  be  theo- 
retically. "  As  a  matter  of  fact,  theory  teaches  in  full  agreement 
with  practice  that  with  insufficient  kinetic  energy  of  the  rotat- 
ing parts  regulation  is  very  poor.  Either  the  governor  hunts 
continually,  or,  if  the  governor  has  been  quieted  down  by  the 
never  failing  remedy  of  an  oil  pot,  excessive  speed  fluctuations 
appear  at  the  time  of  a  change  of  load. 

1  Average  during  one  revolution. 


108    GOVERNORS  AND  THE  GOVERNING  OF   PRIME   MOVERS 


The   remaining   factors   of   equation    (4a) 
upon  properties  of  the  governor.     The  radical 


depend   mainly 

2A0me 

will 


easily  be  recognized  by  comparison  with  equation  (1)  of  Chap- 
ter IV  to  be  the  traversing  time  of  the  governor,  or  rather  that 
traversing  time  which  exists  when  the  centripetal  force  of  the 
governor  has  to  accelerate  not  only  the  masses  of  the  governor 
proper,  but  also  those  of  the  valve  gear  parts  which  are  mechani- 
cally connected  to  the  governor.  This  fact  should  remind 
designers  of  engines  and  turbines  that  the  promptest  governor 
can  be  handicapped  by  being  required  to  move  massive  valve 
gear  parts. 

With  these  simplifications  the  relative  speed  fluctuation  — 
to  either  side  from  mean  —  of  the  limiting  case  boils  down  to 

Ue=    IA_    T_ 

u   "  2A0  T8       p 
so  that  the  total  speed  fluctuation  is 


u 


A0    T.      p 


(5) 


The  only  quantity  in  this  equation  which 
remains  to  be  discussed  is  the  influence  of  p, 
the  static  fluctuation.  Evidently,  the  speed 
fluctuation  grows,  as  p  is  reduced,  which  proves 
conclusively  that  governors  with  small  static 
fluctuation  —  that  is  to  say  with  great  sensi- 
tiveness —  either  produce  hunting  or  else  re- 
quire large  oil  pots.  The  rather  unexpected 
result  that  governors  designed  for  small  speed 
fluctuation  produce  large  speed  fluctuations 
proves  that  the  much  and  long  sought 
isochronous  governor  (p  =  0)  is  impracticable, 
because  the  slightest  change  of  load  produces 
infinitely  great  speed  fluctuations. 
It  is  true  that  isochronous  governors  have  been  successfully 
used  for  speed  regulation,  but  in  every  such  case  the  success 


FIG.  74 


INTERACTION   BETWEEN   GOVERNOR  AND  PRIME  MOVER      109 


is  due  either  to  the  presence  of  tangential  inertia  in  the  governor 
(see  paragraph  3  of  present  chapter),  or  else  to  the  use  of  float- 
ing springs  in  an  oil  pot.  The  latter  device  temporarily  increases 
the  stability  of  the  governor, 
as  will  be  seen  from  the  fol- 
lowing description.  Illustra- 
tion 74  represents  diagram- 
matically  — •  with  intentional 
omission  of  design  features — 
an  oil  pot  with  floating 
springs.  Hole  (1)  in  the 
central  piston  is  large  com- 
pared to  holes  (2)  and  (3)  in 
the  surrounding  box  piston. 
Hence  any  quick  motion  of 
the  piston  rod  deforms 
springs  (4)  and  (5)  so  that  p 
is  temporarily  increased  by 
the  difference  of  the  spring 
forces.  If  the  force  upon  the 
piston  rod  is  not  vibratory, 
but  steady  in  one  direction, 
the  box  piston  adjusts  itself 
quite  gradually  to  the  new 
load,  or  rather  new  position 
of  the  governor,  eliminating 
the  forces  of  the  springs  (4) 
and  (5)  for  static  calculations 
(isochronism)  or  for  final 
effects  of  change  of  load.  Air 
under  the  piston  of  an  ordi- 
nary oil  pot  acts  in  a  similar 
way,  but  it  is  not  dependable  on  account  of  leakage. 

The  yielding  or  compensating  oil  pot  of  Fig.  74  may  be  made 
an  integral  part  of  the  governor  proper.  Two  notable  examples 
of  such  combination  designs  are  the  Chorlton-Whitehead  gov- 
ernor and  the  Bee  governor,  both  of  British  design.  The  prin- 
ciple of  both  governors  is  the  same,  and  it  will  suffice  to  describe 


FIG.  75 


110    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

one,  for  instance  the  Chorlton-Whitehead  governor.  It  is  shown 
in  Fig.  75.  In  the  manufacturer's  own  words  it  acts  as  follows: 
"The  spring  on  one  side  is  divided  into  two  unequal  por- 
tions, a  plate  forming  the  piston  of  an  oil  gag  pot  being  inter- 
posed between  the  two  portions.  The  oil  gag  pot  itself  is  formed 
in  the  weight,  and  is  provided  with  a  small  adjustable  valve, 
by  means  of  which  free  communication  can  be  made  from  the 
gag  pot  to  the  body  of  the  governor.  The  bottom  casing  being 
entirely  filled,  and  the  bottom  portion  about  four  fifths  full  of 
oil,  the  governor  is  ready  for  work,  and  the  action  will  be  as 
follows: 

"If  the  gag-pot  valve  is  wide  open,  so  that  the  oil  has  a  free 
passage  to  and  from  the  interior,  the  gag-pot  piston  will  be 
quite  free  to  move,  and  the  divided  spring  will  behave  as  one 
complete  spring,  the  piston  merely  acting  as  a  washer. 

"The  compound  spring  in  this  condition  is  exactly  equivalent 
to  the  single  spring  in  the  other  weight,  and  both  are  designed 
to  counteract  exactly  the  centrifugal  force  of  the  weights  in 

all  positions  when  running  at 
constant  speed,  —  in  other  words, 
the  governor  is  isochronous,  and  to 
run  when  in  this  condition  would 
cause  it  and  the  engine  to  hunt 
violently,  as  the  governor  would 
have  no  stability. 

"  If,  on  the  other  hand,  the  valve 
be  closed,  the  gag-pot  piston  be- 
comes immovable,  and  puts  the 
shorter  spring  out  of  action.  We 
have  thus  decreased  the  effectual 

length  of  the  spring,  and  the  governor  will  run  with  a  certain 
amount,  say  8  %,  of  the  variation  between  inner  and  outer  posi- 
tions, making  the  governor  very  stable  —  too  much  so,  in  fact, 
for  close  governing. 

"If,  now,  the  gag-pot  valve  be  partly  opened,  a  point  can  be 
found  where  hunting  just  does  not  take  place,  and  still  the 
governor  will  be  in  equilibrium  in  any  position  after  a  certain 
time  has  elapsed,  allowing  the  gag-pot  piston  to  move  to  its 


INTERACTION  BETWEEN  GOVERNOR  AND  PRIME   MOVER     111 

new  place;  in  other  words,  the  governor  will  be  isochronous 
subject  to  a  certain  time  lag,  which  in  practice  amounts  to  two 
or  three  seconds." 

A  very  ingenious  application  of  the  compensating  oil  pot 
to  shaft  governors  was  made  by  Armstrong.  In  his  governor, 
which  is  illustrated  in  Fig.  76,  the  centrifugal  mass  is  not  solid, 
but  contains  a  separate  section  in  the  shape  of  a  roller,  which 
fits  snugly  in  an  oil-filled  cavity  of  the  main  centrifugal  weight. 
If  the  roller  were  fixed  in  the  weight,  the  governor  would  have 
a  considerable  static  fluctuation;  but  the  cavity  for  the  roller 
is  so  located  that  centrifugal  force  acting  on  the  roller  slowly 
moves  it  to  new  position  after  a  change  of  load  and  of  governor 
position,  shifting  the  mass  center  of  the  weight  and  bringing 
the  speed  back  almost  to  its  original  value. 

Equation  (5)  may  be  used  in  connection  with  the  relations 
for  Ta  for  computing  the  weight  of  flywheel  required  per  horse- 
power of  an  engine,  as  follows  : 

lu1       W    tf      550          Wv* 
3  ~  M0  u=''   g  M0  u  550  =  HP  g  550 

From  these  equations  follows  the  weight  per  horsepower 

W       550  gT. 

HP"— 7^ ;-(6) 

where  v  =  wheel  velocity  at  radius  of  gyration.  In  a  numerical 
calculation,  compute  Ts  from  (5)  and  substitute  in  (6). 

To  test  the  applicability  of  equation  (5),  an  example  will 
now  be  figured.  Given:  Maximum  dynamic  fluctuation  =  .08, 

A       1 

change  of  load  50  %,  equivalent  to  —  =  ~,  static   fluctuation 

A.  o      £ 

p  =  .03,  T  g  =  .07.  This  is  the  traversing  time  of  the  governor 
treated  on  pages  45  and  46,  but  corrected  for  mass  of  the  valve 
gear.  To  insure  a  sufficiently  rapid  dying-out  of  the  vibra- 
tions after  a  change  of  load,  the  dynamic  fluctuation  of  the 
limiting  case  (never-ending  vibrations)  must  be  taken  smaller 
than  the  given  maximum  permissible  fluctuation.  For  this 

reason  2  --  will  be  taken  to  be  .06. 
u 


112    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 
With  these  values,  equation  (5)  furnishes 


For  cast  iron  flywheels  an  average  value  of  v  is  80  ft.  /sec.    Then 
W       550  X  32 


lP          6400 


=  2 


In  practice,  weights  varying  from  10  to  70  pounds  are 
installed  per  horsepower  (for  v  =  80  ft.  /sec.).  While  our  result 
agrees  quite  well  with  the  lower  limit  of  the  values  used  in 
practice,  it  is  far  away  from  the  higher  limit.  However,  there 
are  good  reasons  for  the  use  of  heavier  flywheels  than  indicated 
by  our  arithmetical  calculation.  The  principal  ones  among 
these  reasons  are: 

(1)  The  static  stability  of  a  governor  is  seldom  constant 
over  the  whole  range  of  its  travel,  so  that  the  inclination  of 
line   (14)  (15)  in  Fig.  71   varies.     Similarly   the   torque   curve 
(2)  (5)  in  the  same  illustration  is  seldom  a  straight  line.     But 
for  the  use  of  equation    (5)  that  value  of  p  counts  which  is 
derived  from  the  worst  instantaneous  conditions  in  these  two 
curves.     Hence  the  value  of  p  to  be  used  in  equation   (5)  is 
usually  less  than  the  value  of  p  which  is  derived  from  maximum 
and   minimum  speeds   of  the   governor.     In  poorly   designed 
valve  gears  of  engines  and  turbines  the  value  of  p  in  equation 
(5)  may  be  only  TV  of  the  value  derived  from  the  governor. 

(2)  Equation  (5)  presupposes  that  the  governor  is  infinitely 
strong.     Actually  it  must  overcome  resistances  which  at  inter- 
vals block  the  travel  of  the  governor  and  change  its  motion. 
This  problem  is  dealt  with    in    paragraph    4  of  the    present 
chapter. 

(3)  Equation    (5)  is  based  upon  the  assumption  that  the 
action  of  the  governor  is  continuous  and  that  the  effect  of  such 
action  is  instantaneous.    In  reality,  the  governor  can,  in  engines, 
act  only  once  in  every  stroke;   besides,  volume  of  steam  or  of 
explosive  mixture  beyond  control  of  the  governor  delays  governor 
action  in  both  engines  and  turbines,  so  that  heavier  wheels  are 


INTERACTION   BETWEEN  GOVERNOR  AND  PRIME   MOVER     113 

required  for  stability  of  regulation  (see  paragraph  5  of  present 
chapter). 

At  the  conclusion  of  this  paragraph,  a  hint  on  the  size  of 
oil  gag  pots  may  be  valuable.  With  prime  movers  which  are 
subjected  to  frequent  and  heavy  load  changes,  and  with  valve 
gears  which  impress  great  vibratory  forces  upon  the  governor, 
the  oil  gag  pot  of  the  latter  must  dissipate  a  considerable  amount 
of  energy.  If  the  oil  pot  be  small,  the  heat  is  not  radiated 
away  fast  enough,  the  oil  heats  up,  becomes  thin,  and  the  gag 
pot  loses  its  grip.  It  must  then  be  tightened  by  closing  the 
oil  valve.  If  the  oil  pot  is  slightly  too  small,  the  only  harm 
consists  in  the  necessity  of  frequent  adjustments  of  the  oil 
pot,  but  if  the  latter  be  much  too  small,  the  thinning  of  the  oil 
by  the  extreme  heat  will  prevent  the  gag  pot's  furnishing 
enough  damping  power  even  if  the  needle  valve  is  entirely 
closed,  because  the  thin  oil  leaks  between  the  piston  and  the 
cylinder. 

Additional  statements  on  proper  size  of  gag  pot  are  given 
in  paragraph  1  of  Chapter  VIII  and  in  paragraph  4  of  the 
present  chapter. 

References  to  Bibliography  at  end  of  book:  3,  7,  17,  28,  32,  35,  36,  64,  65,  79. 

3.  Influence  of  Tangential  Inertia  in  Governors  upon 
Stability  of  Regulation. —  Study  of  the  limiting  case  affords 
a  good  insight  into  the  effects  which  the  presence  of  weights 
subject  to  tangential  ine/tia  has  upon  the  stability  of  regula- 
tion (see  also  paragraph  2  of  Chapter  II). 

It  was  shown  in  paragraph  2  that,  in  the  limiting  case,  a 
governor  performs  endless  vibrations  of  constant  amplitude, 
with  corresponding  speed  fluctuations  of  the  prime  mover. 
Referring  back  to  illustration  71,  let  the  representative  point 
of  the  governor  be  X  distant  from  the  position  of  power  equi- 
librium, or  in  position  (6)  (8)  (7).  Then  the  prime  mover  is, 

on  account  of  the  sine  harmonic  nature  of  the  vibrations,  being 

X 

accelerated  by  a  torque  which  equals  ~rM  0.    Since  A0,  M0  and 

A  o 

the  rotating  masses  are  constant,  the  acceleration  is  propor- 
tional to  X.    From  paragraph  2  of  Chapter  II  it  is  known  that 


114    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


Static 


FIG.  77 


the  regulating  force  or  torque  of  an  inertia  governor  is  pro- 
portional to  the  angular  acceleration,  as  long  as  the  governor 

does  not  regulate,  or 
else  regulates  slowly. 
In  all  practical  cases  the 
governor  motion  in 
question  is  so  slow  com- 
pared to  the  rotative 
speed  that  its  influence 
upon  the  regulating 
force  can  be  neglected. 
Since  in  the  limiting 
case  the  acceleration  is 
proportional  to  X,  the 
regulating  force  or 

torque,  caused  by  tangential  inertia,  is  also  proportional  to  X. 
Static  regulating  force  in  the  limiting  case,  as  was  shown  in 
paragraph  2  of  the  present  chapter,  is  likewise  proportional  to 
X,  so  that  tangential  inertia  in  this  case  simply  produces  a 
proportional  increase  of 
the  static  regulating 
force  (6)  (8),  as  indicated 
in  Fig.  77  by  the  line 
(20)  (21).  This  latter 
line  takes  the  place  of 
line  (14)  (15)  of  Fig.  71. 
In  the  limiting  case  the 
inclination  of  this  line 
measures  the  force  (resp. 
torque)  per  unit  displace- 
ment accelerating  the 
regulating  motion  of  the 
governor  masses.  Its 
influence  is  measured  in 
the  equations  by  the 
value  of  the  static  fluctuation  up."  The  effect  of  tangential 
inertia  then  is  to  replace  p  in  equation  (5)  of  paragraph  2  by  an 
"  equivalent  static  fluctuation "  p',  involving  both  p  (the 


Centrifugal  Mass 


r 

of  shaft 


FIG.  78 


INTERACTION  BETWEEN   GOVERNOR  AND  PRIME  MOVER     115 

static  fluctuation  proper)  and  a  function  of  the  inertia  masses 
of  the  governor.  The  latter  function  is  given  by  the  relation 
that  the  quantity  which  is  to  be  added  to  p  in  the  shape  of  an 
increase  of  static  fluctuation  must  produce  the  same  regulating 
moment  of  the  governor  masses  which  the  inertia  moment 
produces.  Call  p"  the  added  quantity,  then  the  regulating 

1  \v"u> 

moment  for  removal  of  -  of  the  total  load  is  2  C  h  ~       ~  =  p"  C  ls 

2i  u 

—  (compare  equation  (3)  of  paragraph  1,  Chapter  II),  —  where 
lz  is  the  lever  arm  of  the  centrifugal  mass  about  its  suspension 
point  (see  Fig.  78).  Turning  to  the  inertia  mass,  we  find  that 
removal  of  one  half  of  the  load  produces  an  angular  accelera- 

1  M0, 

tion  of  —  —^  (see  paragraph  2  of  Chapter  II)  ,  and  a  regulating 
2i    L 

moment  equal  to  -  —  ^  —   about   the   suspension   point   of   the 

2i      L 

inertia  weight.  As  before,  I  is  the  moment  of  inertia  of  the 
rotating  parts  of  the  prime  mover,  while  J  is  the  total  moment 
of  inertia  of  the  inertia  mass  about  its  suspension  point.  To 
refer  the  regulating  moment  of  the  inertia  mass  to  the  pivot 

of  the  centrifugal  mass,  multiply  it  by  —  (see  Fig.  78)  .    We  then 


have  P"C13  =  -J 

Zi     1          LI 

k-nn  "     IM°JI* 

from  which  follows  p    =  -  —  p  T—  r- 

2i    L     is  LI 

Finally,  we  obtain  the  equivalent  static  fluctuation 

\M0Jl, 


If  the  rotative  speed  of  the  governor  spindle  differs  from 
that  of  the  engine  or  turbine  shaft,  M0JI  must  be  multiplied  by 
a  factor  involving  the  speed  ratio. 

Since  the  stability  of  regulation  depends  solely  upon  the 
inclination  of  line  (20)  (21),  it  is  quite  immaterial  how  pf  is 
constituted,  and  we  obtain  the  most  interesting  result  that  p 


116     GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

may  be  zero,  or  even  negative,  provided  that  p"  is  large  enough 
to  make  pf  positive.  In  other  words,  if  a  governor  is  built 
with  a  sufficient  amount  of  tangential  inertia,  the  static  fluctua- 
tion may  be  zero  (isochronous  governor),  or  even  negative 
(reversed  speed  curve),  and  yet  the  stability  of  regulation  will 
be  preserved. 

Many  inertia  governors  can  —  and  this  circumstance  is 
well  known  to  operating  engineers  —  be  so  adjusted  that  the 
engine  runs  at  a  higher  speed  with  full  load  than  it  does  at 
no  load.  Between  the  years  1892  and  1905  this  fact  was  widely 
advertised,  so  much  so  that  some  engines  appeared  to  consist 
principally  of  a  wonderful  governor  and  a  few  other,  relatively 
unimportant  parts.  The  total  disappearance  of  these  advertise- 
ments suggests  the  inference  that  regulation  with  a  reversed 
speed  curve  is  of  no  lasting  commercial  value.  Reasons  for 
the  latter  statement  are  apparent. 

For  many  purposes,  particularly  for  parallel  operation  of 
alternating  current  generators,  a  uniform,  positive  static  fluc- 
tuation is  necessary.  A  positive  speed  drop  furnishes  the  only 
means  of  distributing  the  load  between  the  different  generating 
units  in  the  power  plant.  For  this  reason,  prime  movers  for 
alternating  current  generators  are  seldom,  if  ever,  equipped 
with  inertia  governors.  The  rapid  growth  of  central  station 
power  plants  generating  alternating  currents  has  deprived  the 
inertia  governor  of  its  importance.  The  passing  of  the  inertia 
governor  from  the  central  station  should  not  be  misconstrued 
into  the  belief  that  inertia  governors  are  not  suited  to 
alternating  current  work;  they  are  so  suited,  but  they  offer 
no  advantages  whatsoever  except  as  shaft  governors.  For 
mathematical  proof  of  this  statement  refer  to  equation  (4)  of 
paragraph  2  of  present  chapter.  This  equation,  it  will  be 
remembered,  gives  the  speed  fluctuation  of  the  limiting  case. 

/yy\ 

Under  the  radical  stands  the  expression  - — ~  which,  in  words, 

£  p  (_/ 

equals  the  equivalent  governor  mass  divided  by  static  regulating 
force.  To  make  the  speed  fluctuation  small  (that  is  to  say:  to 

W) 

make  regulation  good),  we  must  make  - — °—  very  small.     But 

2i  j)  C 


INTERACTION  BETWEEN  GOVERNOR  AND   PRIME  MOVER     117 

in  the  case  of  the  inertia  governor,  equivalent  governor  mass 
includes  not  only  centrifugal  masses,  but  also  the  mass  of  the 
inertia  weights,  so  that  me  is  increased,  which  is  undesirable. 
If  tangential  inertia  of  centrifugal  masses  is  utilized,  instead 
of  using  separate  centrifugal  and  tangential  masses,  the  equiva- 
lent mass  is  increased  just  the  same,  because,  for  a  given  product 
of  centrifugal  force  times  radial  path  of  this  force,  the  product 
of  total  mass  times  total  travel  of  mass  must  be  increased  over 
what  it  would  be  if  the  weights  traveled  radially,  in  which  latter 
case  they  are  subjected  to  centrifugal  force  only,  but  not  to 
tangential  inertia.  On  the  other  hand,  the  regulating  force 
has  also  been  increased  by  the  addition  of  inertia  force.  Thus 
both  numerator  and  denominator  of  what  may  be  termed  the 
promptness  factor  have  been  increased.  Evidently,  addition 
of  tangential  inertia  is  useful,  where  reduction  of  p  to  a  very 
small  value  is  demanded,  because  it  keeps  the  denominator  of 
the  promptness  factor  from  becoming  almost  zero.  But  where 
p  must  have  a  definite,  positive  value,  say  from  .02  to  .04, 

total  equivalent  mass 

the  fraction  -  .  ,. cannot  be  reduced  by  the  ad- 

total  regulating  force 

dition  of  tangential  inertia.  Attention  is  again  called  to  the 
fact  that  this  fraction  represents  the  "quality  factor"  of  the 
governor  in  equations  (4)  and  (4a)  of  paragraph  2.  Nothing 
can  be  gained  by  application  of  tangential  inertia  to  the  spring- 
loaded,  high-speed  governors  of  our  modern  steam  turbines, 
hydraulic  turbines,  and  gas  engines. 

The  logical  conclusion  to  be  drawn  from  this  reasoning  is 
that  tangential  inertia  should  be  limited  to  shaft  governors 
which  have  to  handle  heavy  valve  gears.  See  also  paragraph  1 
of  Chapter  VIII. 

References  to  Bibliography  at  end  of  book:  2,  7,  32,  33,  36,  43,  65. 

4.  Solid  Friction  as  a  Damping  Agent.  —  Wischnegrad- 
sky's  theorem  that  stable  governing  is  impossible  without  the 
use  of  an  oil  gag  pot  was  not  taken  seriously  by  engineers 
at  the  time  of  its  publication,  because  of  the  great  number 
of  governors  working  satisfactorily  and  giving  excellent  regu- 
lation without  the  use  of  an  oil  brake.  At  the  same  time, 


118    GOVERNORS  AND  THE   GOVERNING   OF  PRIME   MOVERS 


governors  in  those  days  (1877)  were  not  free  from  friction.  The 
thought,  therefore,  suggests  itself  that  solid  friction  may, 
under  certain  conditions,  satisfactorily  take  the  place  of  liquid 
friction. 

Unfortunately,  the  exact  calculations,  as  soon  as  solid  fric- 
tion is  substituted  for  liquid  friction,  become  so  complicated, 
even  in  the  comparatively  simple  limiting  case,  that  we  must 
be  satisfied  with  approximations.  Three  cases  will  be  con- 
sidered, —  first,  that  of  friction  caused  by  compound  centrifugal 

force;  second,  the  case  of 
constant  friction;  and  third, 
the  case  of  friction  which  is 
greater  at  rest  than  it  is  dur- 
ing motion. 

For  the  purpose  of  study- 
ing the  action  of  compound 
centrifugal  force  (sometimes 
called  Coriolis'  force),  sup- 
pose that  in  the  governor  of 
which  Fig.  79  is  a  plan  view, 
two  weights,  each  of  mass  m, 
are  rotating  with  an  angular 
velocity  u.  The  springs 
are  so  dimensioned  that  they  balance  the  centrifugal  forces 
of  the  weights  in  any  position.  Let  the  weights  move  out- 
ward with  a  linear  velocity  v.  Then  a  force  is  exerted  between 
each  weight  and  its  guiding  wall  by  reason  of  two  sepa- 
rate actions.  First,  the  weight  moves  into  a  larger  orbit  so 
that  its  absolute  velocity  must  be  increased;  and  second,  the 
absolute  velocity  of  each  weight  changes  its  direction.  In 
time  dt  the  radius  of  the  orbit  of  the  weight  is  changed  from 
r  to  r  +  v  dt  which  means  that  the  peripheral  velocity  of  the 
weight  is  increased  from  u  r  to  u  (r  +  v  dt)  so  that  change 
of  velocity  dv  —  u  v  dt.  But  force  X  time  =  mass  X  change  of 
velocity,  or  in  symbols  Qidt  =  muvdt,  and  Qi  =  m  u  v  for 
each  weight.  In  the  same  time  dt  the  velocity  v  has  been 
turned  through  the  angle  u  dt.  Figure  80  shows  that  the 
change  of  velocity  is  u  v  dt  from  which  follows  the  accelera- 


FIG.  79 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME    MOVER     119 

tion  u  v  dt/dt  =  u  v,  and  the  force  Q2  =  m  u  v  for  each  weight. 
The  total  force  exerted  by  each  weight  against  its  guiding  sur- 
face equals  the  sum  Qi  +  Qz  =  2  m  u  v.  The  force  which  each 
moving  weight  exerts  against  the  constraining  side  wall  is 
directly  proportional  to  the  velocity 
v  of  the  vibrating  motion.  If  we 
now  assume  that  the  coefficient 
of  friction  is  constant,  then  we 
find  that  the  damping  friction  is  Ancjle^  U-dt. 
also  directly  proportional  to  the  FIG<  go 

velocity  of  vibration  of  the  govern- 
or. If,  therefore,  all  other  friction  be  eliminated  and  only  that 
friction  which  is  caused  by  compound  centrifugal  force  be  allowed 
to  act,  then  and  in  that  case  the  damping  action  is  identical  with 
that  furnished  by  liquid  friction.  If,  in  addition,  the  coefficient 
of  friction  is  of  such  magnitude  that  2fmuv  just  equals  the 
dynamic  regulating  force,  all  conditions  which  are  necessary 
for  the  limiting  case  are  fulfilled,  and  all  the  calculations  of 
paragraph  2  of  the  present  chapter  apply  without  change. 

Friction  caused  by  compound  centrifugal  force  is  present 
in  every  governor  with  practically  no  exception.  If,  for  in- 
stance, the  governor  illustrated  in  Fig.  2  is  considered,  it  will 
be  seen  that  compound  centrifugal  force  tends  to  bind  the  joints 
at  the  top  of  the  spindle  across  the  corners  to  such  an  extent 
that  a  very  effective  damping  action  is  secured  —  often, 
however,  at  the  expense  of  rapid  wear  in  case  of  repeated  sudden 
changes  of  load. 

In  practice,  friction  due  to  compound  centrifugal  force  can 
never  entirely  take  the  place  of  the  oil  gag  pot,  because  it  is 
not  adjustable.  Since  the  value  of  the  friction  force  isZfmuv, 
adjustment  could  be  secured  only  by  variation  of  the  friction 
coefficient  /;  and  such  variation  at  the  will  of  the  operator  is 
difficult,  if  not  impossible.  Nevertheless,  the  force  under  dis- 
cussion is  helpful,  and  any  complications  in  governor  design 
for  the  purpose  of  eliminating  this  friction  are  not  only  super- 
fluous, but  entirely  out  of  place.  Friction  by  compound  cen- 
trifugal force  is  probably  responsible  for  the  correct  action 
of  many  governors  without  oil  pots  and,  at  least  partly  so,  for 


120    GOVERNORS  AND  THE  GOVERNING  OF   PRIME   MOVERS 


the  lack  of  confidence  placed  in  Wischnegradsky's  theories  at 
the  time  of  their  publication. 

In  the  majority  of  governors  and  governing  devices,  many 
forces  in  addition  to  compound  centrifugal  force  produce  solid 
friction.  For  the  purpose  of  studying  the  effect  of  the  latter, 
let  us  assume  for  a  while  that  the  resistance  caused  by  friction 
is  constant  over  the  whole  travel  of  the  governor. 

Referring  back  to  Fig.  71,  we  remember  that  the  limiting 
case  consists  of  continued  vibrations  of  constant  amplitude 

about  the  position 
of  equilibrium. 
We  also  remember 
that  this  condition 
is  brought  about 
by  dissipating  (by 
means  of  some 
damping  force)  the 
work  done  by  the 
dynamic  regula- 
ting force.  Figure 
81,  which  illust- 
rates the  limiting 
case  with  constant 


(path  of  representative  point) 
FIG.  81 


solid  friction  as  a 
The  principal  addi- 


damping  agent,  is  very  similar  to  Fig.  71. 
tion  is  the  line  (9)  (15),  which  has  been  drawn  in  such  a  way 
that  the  work  areas  shaded  horizontally  and  vertically  are 
equal,  which  makes  the  rectangle  (11)  (9)  (15)  (13)  equal  to  the 
half  ellipse  (11)(18)(13).  At  this  point  the  approximation 
begins.  With  solid  friction,  curve  (11)  (18)  (13)  cannot  be  an 
exact  ellipse,  because  the  latter  is  based  upon  the  equality  (at 
any  time)  of  dynamic  regulating  force  and  of  damping  force. 
However,  the  difference  between  the  ellipse  and  the  curve  re- 
placing it  will,  except  under  special  conditions  explained  below, 
be  so  small  that  we  may  well  use  the  ellipse  as  an  approxima- 
tion; the  true  curve  most  certainly  must  have  a  horizontal 
tangent  at  point  (18). 

With  the  work  of  the  dynamic  regulating  forces  dissipated 


INTERACTION    BETWEEN   GOVERNOR   AND   PRIME   MOVER     121 

by  friction,  the  governor  moves  under  the  influence  of  the 
static  regulating  force  only.  The  vibrations  are  very  nearly 
sine  harmonic,  with  constant  amplitude.  It  is,  therefore, 
apparent  that  solid  friction,  on  general  principles,  can  serve 
for  damping  governor  vibrations.  This  statement  must  be 
qualified  by  the  restricting  explanationHhat  there  are  two  vital 
differences  between  liquid  friction  (including  the  equivalent 
action  of  friction  by  compound  centrifugal  force)  and  con- 
stant frictipnal  resistance.  The  first  difference  is  that,  while 
with  an  oil  pot  stability  can  be  enforced,  even  if  the  static 
fluctuation  is  infinitely  small,  there  exists  with  solid  friction 
a  minimum,  below  which  the  static  fluctuation  cannot  be  re- 
duced, if  stability  is  to  be  preserved.  The  second  difference 
is  that,  with  solid  friction,  there  occur  continuous  speed  fluc- 
tuations no  matter  whether  the  load  varies  or  remains  constant. 
For  proof  of  the  assertion  that,  with  solid  friction,  stability 
requires  a  minimum  value  of  the  static  fluctuation,  again 
study  Fig.  81.  As  before,  (11)  (18)  (13)  is  the  near-ellipse  of 
dynamic  regulating  forces,  (11)  (9)  =  (13}  (15}  is  the  constant 
damping  force  of  friction  so  that  area  (11}  (9}  (15}  (13}  equals 
area  (11}  (18}  (13}  which  (from  the  well-known  formula  for 

the  area  of  an  ellipse)  means  that  (11}  (9}  =  —  (10}  (18}.      Let 

(11}  (13}  equal  the  whole  travel  of  the .  representative  point  of 
the  governor.  Then  line  (14)  (15}  indicates  the  regulating 
forces  caused  by  the  smallest  allowable  static  fluctuation  p. 
The  motion  of  the  governor  could  not  be  continuous,  if  p  were 
smaller  than  here  shown;  for,  if  (11)  (14)  were  smaller  than 
(11)  (9),  there  would  not  be  enough  regulating  force  at  either 
end  of  the  governor  travel  to  start  it.  The  two  halves  (11) 
(18)  (13)  and  (18)(19)(ll)eoithe  near-ellipse  would  be  pulled 
apart  up  and  down  in  the  illustration.  Area  (11)  (9}  (15)  (13} 
of  the  damping  forces  then  would  no  longer  equal  the  area  of 
the  dynamic  regulating  forces,  and  the  speed  would  fluctuate 
between  wider  and  wider  limits. 

The  mathematical  determination  of  the  smallest  static 
fluctuation  which  is  allowable  with  solid  friction  as  a  damping 
force  must  evidently  start  from  the  relation  that  the  static 


122    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 
regulating    force     (11)  (14)     equals    damping    force     (11)  (9), 
which  latter  equals  --  times  regulating  force    (10)  (18).     But 
(10)  (18)  is  caused  by  ue  of  equation  (5)  of  paragraph  2.    The 

cited  equation  is  -  -  — ^  y  -•      For  the  conditions  indi- 

u         2i  A.  o  1  s       p 

A        1 
cated  in  Fig.  81  (governor  swinging  from  stop  to  stop)  -  -  =  -• 

A.  o       £ 

Since  the  damping  force   (11)  (9)  only   serves   the  purpose   of 
relating  speed  difference  (14)  (11)  to  speed  difference  (10)  (18), 


we  conclude  that 

and 

or  finally 


u 


2      4  2  2  Ts 

8rrt 
*    s 


16 


(1) 


This,  as  before  stated,  is  the  smallest  permissible  static  fluctua- 
tion, if  solid  friction  of  constant  magnitude    (referred  to  the 
^  representative  point) 

1  is  employed,   and  if 

the  governor  has  con- 
stant stability  over 
its  whole  travel. 
This  latter  condition 
is  seldom  fulfilled  so 
that  actually  the 
smallest  permissible 
value  of  p  must 
exceed  that  found 
_  from  equation  (1). 

-Total  t ravel  of  govern or—J  ft    is    interesting    to 

(path  of  representative  point; 


FIG.  82 


note  that  p  can  be 
the  smaller,  the 
prompter  the  governor  (T g  small),  and  the  greater  the  moment 
of  inertia  of  the  rotating  masses  of  the  prime  mover  compared 
to  the  capacity  of  the  latter  (T8  long). 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME    MOVER     123 

For  proof  of  the  second  assertion,  namely  that  constant 
friction  as  a  damping  agent  results  in  never-ending  vibrations, 
even  at  constant  load,  refer  to  Fig.  82,  which  is  similar  to  the 
preceding  illustrations,  but  is  more  complete.  The  outer 
curve  (11)  (18)  (13)  (19)  is,  as  before,  the  near  ellipse  of  the 
forces  caused  by  the  speed  changes  resulting  from  a  sudden 
change  of  50%  of  the  total  load.  (9)  (15)  is  the  line  of  con- 
stant friction  resistance.  Now  let  the  engine  or  turbine  operate 
at  a  little  above  half  of  maximum  load  (governor  position  (21)), 
and  let  the  load  be  suddenly  reduced  to  exactly  one  half  of 
maximum  load.  Then  the  governor  will,  in  the  limiting  case, 
vibrate  in  the  range  (21)  (22).  However,  the  static  regulating 
force  now  is  small  compared  to  the  resisting  friction,  and, 
before  motion  of  the  governor  can  begin,  the  speed  must  rise, 
until  a  dynamic  regulating  force  (21)  (23)  has  been  produced 
which  is  determined  by  the  equation  (23)  (2Jf)  =  (21)  (2 5). 
The  relation  between  governor  motion  and  speed  of  prime 
mover  is  given  by  the  near  ellipse  (23)  (26)  (27).  At  this  last 
point  the  governor  is  detained  by  friction;  the  speed  must 
drop  through  a  range  corresponding  to  the  distance  (27)  (28) 
before  the  return  stroke  of  the  governor  can  take  place.  The 
motion  is  intermittent,  discontinuous.  Now  let  the  change 
of  load  become  smaller  and  smaller.  Then  the  curve  of  motion 
will  finally  shrink  into  the  line  (29)  (30),  which  means  that 
even  at  constant  load  there  will  be  a  continued  speed  fluctuation 
of  sufficient  magnitude  to  overcome  frictional  resistance. 

Whenever  the  just  described  conditions  are  realized  in 
practice,  the  speed  fluctuation  is  even  greater  than  is  indicated 
by  the  distance  (29)  (30),  because  the  latter  equals  twice  the 
minimum  friction  necessary  for  stability  with  endless  vibra- 
tions for  50  %  change  of  load,  and  because  in  practice  a  some- 
what greater  friction  will  be  provided  for  safety. 

From  the  foregoing  explanations  it  is  evident  that  solid 
constant  friction  as  a  damping  agent  for  governors  is  rather 
undesirable  under  the  assumed  conditions.  However,  it  will 
do,  after  a  fashion.  On  the  other  hand,  friction  which  is  greater 
between  surfaces-at-rest  than  it  is  between  surf  aces- in-relative- 
motion  will  not  do  at  all,  as  may  be  seen  from  Fig.  83.  If  the 


124     GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


governor  is  suddenly  displaced  the  distance  (2)  (3)  from  posi- 
tion of  equilibrium  and  is  then  released,  friction  of  rest  holds 
it.  As  before,  the  speed  must  rise  to  a  value  indicated  by  point 
(4))  determined  by  the  relation  (4)  (£)  =  C0(#)>  before  motion 
can  begin.  As  soon  as  motion  is  under  way,  the  dynamic 
regulating  force  grows  —  see  curve  (4)  (6)  —  while  the  damp- 
ing force  of  friction  drops  rapidly.  The  work  of  the  dynamic 
regulating  force  cannot  be  dissipated  by  the  damping  force  of 
friction,  and  the  vibrations  increase  in  amplitude,  until  one  of 
the  limiting  stops  is  struck. 

If  solid  friction  really  acted  as  indicated  by  Figs.  82  and  83, 
Wischnegradsky's  theorem  of  the  necessity  of  an  oil  gag  pot 

would  not  have  been 
doubted  at  the  time 
of  its  publication. 
But  as  a  matter  of 
fact  it  is  extremely 
difficult  to  make  solid 
friction  behave  in  the 
above  assumed  man- 
ner. It  can  be  done 
in  a  governor  regulat- 
ing a  very  well-bal- 
anced  steam  or 
hydraulic  turbine,  said 
governor  being  driven 


(path  of  representative  poll 
FIG.  83 


by  well-hobbed  gears  running  in  oil,  and  said  governor  being 
entirely  free  from  impressed  vibrations.  But  these  ideal  condi- 
tions did  not  exist  and  could  not  be  produced  in  1877.  Steam 
and  gas  engines  with  considerable  cyclical  speed  fluctuation  were 
the  principal  prime  movers.  Governors  were  driven  by  belts  or 
by  inaccurately  cut  gears;  and  most  governors  were  sub- 
jected to  impressed  vibratory  forces.  We  shall  presently  see 
that  under  such  conditions  solid  friction  is  indeed  quite  fre- 
quently equivalent  to  an  oil  gag  pot. 

For  the  sake  of  simplicity  consider  instead  of  a  governor 
a  particle  of  mass  m  which  is  moved  back  and  forth  by  a  force 
Q  reversing  its  direction  every  t  seconds.  Let  the  motion  be 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME    MOVER     125 

resisted  by  a  frictional  force  F  which  is  quite  small  compared 
to  Q.  Then  total  change  of  velocity  between  opposite  direc- 

Qt 
tions  of  motion  equals  —  ;    maximum  velocity  in  each  direc- 

7YI 

tion  equals  -  -  -  and  average  velocity  in  each  direction  equals 

2i    Tfl 

— .    Hence,  the  total  displacement  of  the  vibrating  particle 

1  Qt 2 
equals  -  -  — .     Now  let  a  small,   constant  force  Qi  which  is 

smaller  than  the  friction  force  F,  act  upon  the  particle  ra  in 
the  direction  of  its  vibratory  motion.  Then  the  center  of 

IQ? 
QiX~ 

4   m 

vibration  is  shifted  the  distance  -    — every  half  vibration  ; 

r 

for  proof,  see  paragraph  2  of  Chapter  VIII.  The  particle, 
therefore,  moves  forward  with  an  average  velocity  v  = 

which  may  be  written  v  =  K  Qi,  where  K  is  a  proportionality 
factor.  The  " average"  forward  velocity  of  the  jerky  motion 
is  proportional  to  the  moving  force,  from  which  we  conclude 
that  the  equivalent  resistance  is  also  proportional  to  the 
velocity,  for,  if  it  were  not,  the  velocity  could  not  remain  con- 
stant for  a  given  Qi,  but  would  change. 

Under  the  described  conditions  solid  friction  is  absolutely 
equivalent  to  an  oil  gag  pot.  While  the  conditions  are  some- 
what idealized,  the  action  of  the  forces  impressed  upon  the 
governor  by  many  valve  gears  is  sufficiently  close  to  the  ideal 
case  to  make  the  latter  dependable  for  practical  conclusions. 
The  diagram  of  one  complete  vibration  will,  in  the  language 
of  the  other  illustrations  of  this  paragraph,  look  somewhat  like 
Fig.  84,  the  number  of  zigzags  depending  upon  the  relative 
frequencies  of  impressed  vibration  and  natural  vibration.  Since 
it  is  somewhat  difficult  to  visualize  the  diagram  84,  a  tachometer 
record  taken  from  a  steam  engine,  and  showing  the  same  action, 
is  reprinted  in  Fig.  85.  The  upper  curve  represents  the  motion 
of  the  governor,  and  the  lower  curve  illustrates  the  speed  flue- 


126    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


tuation  of  prime  mover  and  governor.     The  governor  was  on 
purpose  subjected  to  greater  impressed  forces  than  will  ever 

occur  in  practice. 
These  forces  were 
not  the  same  at  all 
loads,  which  ac- 
counts for  the  dif- 
ference in  the  gov- 
ernor motion  before 
and  after  the 
change  of  load. 

Governor  travel *-  The     mathema- 

tically treated  ideal 
case  does  not  hold, 
if  the  regulating  force  Qi  is  greater  than  the  resisting  friction  F, 
because  the  average  velocity  then  grows  continually,  and  the 
equivalence  of  solid  friction  and  liquid  friction  is  lost.  To 


CDO 

ee 

<   0 


FIG.  84 


Speed  of  Engine 


y^^s^ 


FIG.  85 


again  make  F  exceed  Qi  in  value,  the  former  may  be  increased, 
but  there  are  limits,  because  the  impressed  force  Q  must  stay 
great  compared  to  the  friction  force  F,  to  preserve  proportion- 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME    MOVER     127 


ality.  Fortunately,  friction  due  to  compound  centrifugal  force 
steps  in  helpfully  just  about  at  the  place  where  solid  friction 
of  the  vibrating  system  leaves  off. 

In  addition  to  the  case  of  a  vibrating  governor,  there  is 
another  set  of  circumstances  under  which  solid  friction  acts 
very  much  like  liquid  friction,  viz.  the  case  of  a  governor  in 
which  solid  friction  of  considerable  magnitude  is  alternately 
applied  and  removed,  for  instance  by  jar  or  vibration.  To  treat 
this  case  mathematically  assume  that  the  governor  is  absolutely 
free  from  friction  during  t  seconds  and  is  held  by  quite  great 
friction  during  the  next  t  seconds,  and  so  on.  During  each 
free  period  the  governor  —  which  we  will  replace  by  a  particle 

of  mass  m  —  reaches  a  final  velocity ,  where  Qi,  as  before, 

is  the  regulating  force.  This  velocity  is  then  almost  instantly 
dissipated,  and  the  governor  remains  at  rest  during  the  next 
t  seconds.  The  average  velocity  is,  therefore,  one  quarter  of 

the  above  value,  or  average  v  =  -      — .    Again,  the  average  ve- 

4   in 

locity  is  proportional  to  the  regulating  force  so  that  the  action 
of  heavy  friction 
applied  at  intervals 
and  relieved  at  in- 
tervals closely  re- 
sembles the  action 
of  an  oil  brake. 
The  regulation  dia- 
gram of  the  limiting 
case  will  look  some- 
what like  Fig.  86, 
the  number  of  steps 
depending  upon  the 
ratio  of  the  frequencies  of  friction  releases  and  of  natural  vibra- 
tion of  governor. 

While  the  just  explained  method  of  damping  is  effective,  it 
is  not  as  efficient  as  an  oil  brake,  because  it  produces  greater 
speed  fluctuations.  It  very  much  increases  the  time  of  natural 
vibration  of  the  governor,  because  the  latter  has  to  start  from 


Ol 


coo 


> 
1° 


Governor  iravel  - 
FIG.  86 


128    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

rest   after   each   stoppage.      However,   satisfactory   regulation 

T 'g 
can  be  obtained  in  spite  of  this  drawback,  if  the  ratio  -—-  is 

J-  s 

made  quite  small. 

It  is  now  evident  that  the  practical  engineers  who  objected 
to  Wischnegradsky's  theorem  on  the  ground  that  so  many 
governors  worked  well  without  gag  pots  were  right  in  their 
practical  observations.  But  they  did  not  realize,  first,  that 
the  governors  to  which  they  pointed  as  examples  of  correct 
regulation  without  damping  by  liquid  friction  were  damped 
by  other  agencies,  particularly  by  solid  friction  and,  second, 
that  solid  friction  works  well  only  on  condition  that  its  action 
is  made  equivalent  to  that  of  an  oil  gag  pot. 

We  may  add  that,  the  more  uniform  the  angular  velocity 
of  the  prime  mover,  the  freer  the  latter  from  vibration,  the 
smoother  the  drive  of  the  governor,  and  the  freer  the  latter  from 
impressed  vibrations  on  the  one  hand,  the  smaller  is,  on  the  other 
hand,  the  value  of  solid  friction  as  a  damping  agent,  and  the 
more  must  we  approach  a  frictionless  governor  with  liquid  fric- 
tion for  damping.  And  such  is  indeed  the  trend  of  evolution 
in  the  governing  of  modern  steam  turbines  and  hydraulic 
turbines. 

References  to  Bibliography  at  end  of  book:  28,  36,  65. 

5.  Greatest  Speed  Fluctuation  with  Direct-Control  Gov- 
erning. —  In  the  sales  specifications  of  engines  and  turbines 
the  following  clause  is  frequently  used  with  regard  to  regula- 
tion, "  If  A  per  cent  of  the  rated  load  are  suddenly  removed 
or  put  on,  the  speed  will  not  vary  more  than  B  per  cent  either 
way  from  mean  speed."  No  standard  values  for  A  and  B  have 
ever  been  adopted  by  engine  and  turbine  builders,  but  the 
common  use  of  this  clause  is  proof  that  there  exists  a  definite 
practical  demand  for  computing  the  speed  fluctuation  of  at 
least  the  first  wave  after  a  disturbance.  Unfortunately  the 
analytical  calculation  is  extremely  unsatisfactory  from  a  prac- 
tical standpoint.  To  get  an  analytical  expression,  many  as- 
sumptions must  be  made,  and  even  then  the  calculation  is 
far  from  simple;  so  far  from  it,  in  fact,  that  it  deters  all  engi- 


INTERACTION    BETWEEN    GOVERNOR   AND    PRIME   MOVER     129 


neers  with  the  possible  exception  of  a  few  governor  specialists. 
In  spite  of  this  condition  the  elements  of  the  analytical  calcu- 
lation will  be  given  in  the  present  chapter,  because  they  afford 
a  very  good  insight  into  the  mechanism  of  regulation. 

The  assumptions  are  the  same  as  those  made  in  the  pre- 
ceding paragraphs  of  this  chapter,  namely  that  the  action  of 
the  governor  is  continuous,  that  there  is  no  time  lag  due  to 
stored-up  fluid  energy  beyond  control  of  the  governor,  and  that 
all  resisting  friction  is  equivalent  in  its  action  to  an  oil  gag  pot. 

Figure  87  shows  the  relations  between  the  factors  entering 


Ao= 

maximum 
governor 
travel 


/  /UQ  old 

ZZ~; 


/Maximum  \ 
V  torque    / 


FIG.  87 


into  the  equations.  Let  both  prime  mover  and  governor 
work  in  equilibrium  with  initial  or  "old"  torque  M0,  and  let 
the  resisting  or  counter  torque  suddenly  be  reduced  to  a  "new" 
value  Mn.  Then  the  torque  (M0  —  Mn)  is  unbalanced,  and  the 
speed  rises  as  indicated  by  curve  (1)(2).  Under  the  influence 
of  unbalanced  centrifugal  force  and  of  tangential  inertia  the 
governor  moves,  as  indicated  by  curve  (1)(4)>  The  lag  of  the 
governor  motion  (1)(4)  behind  the  speed  change  (!)(£)  is,  of 
course,  due  to  its  mass. 

When  the  governor  has  reached  position  (4),  the  unbalanced 

torque  is  M  =  -   -  Mm.     The  ordinate  x  is  measured  from  the 


130    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

new  position  as  a  basis,  because,  as  will  be  seen  later,  the  gov- 
ernor has  a  tendency  to  perform  vibrations  about  the  new 
position.  The  minus  sign  is  used,  because  in  the  chosen  posi- 
tion M  is  positive,  and  x  is  negative,  so  that  the  negative  sign 
is  required  to  make  M  positive.  From  the  fundamental  rela- 
tion that  rate  of  change  of  angular  velocity  equals  unbalanced 

du      —x  Mm 
torque  divided  by  moment  of  inertia,  we  have  —  =  —  — p- • 

dt          A.  o      JL 

To  make  this  equation  applicable  to  all  cases,  we  introduce  the 

x 
following  notations:       '-  =  X  =    relative  change  of    governor 


position,    and    =  U  =  relative     speed    change;      then 


du  =  d(u  —  un)  =  un  -  —  =  un  dU,  from  which  we  derive 

Un 

un  —  =  —  X—  ^-  ;  but  as  formerly  (in  paragraph  2)  we  have  the 
at  1 

u  I 

starting  time  Ts  =  -rr-.    Throughout  this  calculation  we  neglect 
M.  m 

the  (comparatively)  very  small  difference  between  u  and  un, 
and  finally  obtain  the  equation  for  the  "  rate  of  change  of  speed 
deviation  "  in  the  following  simplified  form: 


m 

dt          2V 

On  the  governor  act  (1)  unbalanced  centrifugal  force,  (2) 
tangential  inertia,  (3)  damping  resistances.  Turning  first 
to  the  centrifugal  forces,  we  note  that  in  the  position  under 
consideration  the  speed  (2)  (4)  is  unbalanced.  In  the  illustra- 
tion, the  scale  for  velocities  has  been  so  related  to  the  scale  of 
governor  positions  that  the  curve  showing  the  latter  also  repre- 
sents the  curve  of  equilibrium  speeds  of  the  governor.  At 
point  (5)  the  governor  has  reached  its  correct  position,  but  the 
actual  speed  having  reached  point  (6>),  there  is  still  a  force 
urging  the  governor  on.  Going  back  to  position  (4),  we 
recognize  that  the  distance  (2)  (3)  represents  the  speed  dif- 
ference producing  the  dynamic  regulating  force  (due  to  "wrong 


INTERACTION    BETWEEN    GOVERNOR   AND    PRIME    MOVER     131 


m( 


speed  ")  and  that  (3)  (4)  represents  the  speed  difference  pro- 
ducing the  static  regulating  force   (due  to  " wrong  position"). 

x 
The  speed  difference  driving  the  governor  is  thus  (u—un)——pun- 

The  second  term  is  positive,  because  x  itself  is  negative.    The 
force  driving  the  governor  then  is  2C  ( -     — — —p 

\      Un  A0     > 

if  we  refer  the  motion  to  radial  travel  of  the  governor.  The 
motion  may  be  referred  to  the  sleeve,  in  which  case  C  is  replaced 
by  the  strength  P,  or  it  may  be 
referred  to  angular  swing  of  weight 
arm,  in  which  case  C  is  replaced  by 
spring  moment  of  governor.  It  is 
evident  that  the  speed  relation  be- 
tween prime  mover  shaft  and  gov- 
ernor spindle  drops  out  of  the  equa- 
tion, because  we  deal  only  with 
relative  speed  changes. 

For  the  sake  of  completeness  let 
us  consider  a  combined  centrifugal 
and  inertia  governor  of  any  one  of 
the  types  illustrated  in  paragraph  2 
of  Chapter  II.  The  diagrammatic 
drawing  of  such  a  governor  (Fig.  88)  will  assist  in  deriving  the 
equations.  From  paragraph  2  of  Chapter  II  it  is  known  that  the 

du 
inertia  regulating  moment  is  —  (ra  r  L+J) .    The  governor  shown 

in  Fig.  88  is  of  a  simple  type,  in  which  mrL  =  0,  so  that  the 

du        du 

regulating  moment  is  reduced  to  —  J  =  — -  m»  Li2.   Note  that  the 

at         at 

du 

moment  for  positive  —  produces  a  positive  change  of  #,  that 
at 

is  to  say  it  moves  the  centrifugal  weight  away  from  the  axis 
of  rotation.    If  all  equations  are  referred  to  radial  motion,  the 

du      Li2 

force  exerted  by  tangential  inertia  is  ~rr'nii~r~  at  point  (1),  and 

dt       Jui 

un  du      LI  Z/2 

—  mi—     ~at  the  mass  center   of   the  centrifugal  weight. 

Un     dt  LZ 


FIG.  88 


132    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

This  expression  for  the  regulating  force  due  to  tangential  inertia 

dU  LiL2 

may  be  written    —  un  m*  —  — 
at  L/3 

The  force  exerted  by  an  oil  gag  pot  or  by  equivalent  solid 
friction  appears  in  the  form—  K—  or  —  K  —  —  A0.     It  has  the 

negative  sign  because  it  opposes  increase  of  x.  Adding  up 
we  obtain  the  sum  of  all  unbalanced  forces  acting  upon  the 
governor,  namely 


This  sum  of  forces  equals  equivalent  mass  (me)  1  times  accelera- 
tion so  that  we  obtain 

d*x  LiL2  dU  dX 

me-:r^  =  2C(U-Xp)  +  unmi  —  --  —-K  A0—- 
di  L/3    at  at 

Further  developments  will  show  that  the  character  of  the 
regulation  depends  upon  the  relation  between  certain  time 
elements.  With  two  of  these  we  are  familiar,  namely  the 
starting  time  TS)  and  the  governor  traversing  time  T  g.  To 
introduce  the  latter,  divide  the  equation  by  2  C  ;  then  the  left- 

meA 

~  2m( 
Chapter  IV)   so  that  the  left-hand  member  can  be  written 

*d?X  ',  UnmtLnL* 

Similar  time  values  can  be  introduced  for 


hand  member  becomes  -  f^  "T^T ',    but  A0  =  ---T?    (see 


m 


0  „ 

at2  2  C 


and  for         * ;    studying  the  latter  expression,  we  realize  that 

C 

—  is  that  velocity  which  an  unbalanced  force  C  would  finally 

K 

KA 
produce  when  opposed  by  the  oil-brake.     And     „  °  is  the  time 

which  is  required  to  traverse  the  whole  travel  A  0  of  the  governor 

1  me  in  this  case  equals  mc  +  n 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME   MOVER     133 

c 

with  said  velocity  —  •     This   time   may   be   called   the   brake- 
A 

resistance  traversing  time.     It  will  be  denoted  by  Tb,  so  that 

—7  =  -  Tb.     Similar  reasoning  can  be  applied  to  the  expres- 
2  C       2 

UnWliLiLz 

sion  —  ^-777  --  un  LI  is  the  linear  velocity  of  the  inertia  mass  m\. 
2 


CL3 

A  centrifugal  force  C  would  exert  the  force  ~  —  on  this  mass,  so 

L/2 

CT  Ij 

that          -  is  a  linear  acceleration.      C~  —  Tt  =  un  LI  where  7\ 


might  be  called  the  starting  time  of  the  inertia  mass.     Hence 

Wn77l;Z/iZ/2          Ti 

—  =  —  •     With  these  notations  the  equation  of  motion 
2  CL/3          2 

of  the  governor  masses  is 


IT  A2  &X  T<dU      Tb  dX 

"        +         =  0----  2 


2  /     a^2  2    at        2    at 


Equations  (1)  and  (2)  contain  U  and  X.  We  can  eliminate 
one  at  will  and,  by  doing  so,  obtain  the  final  differential 
equation  either  for  X  (governor  deviation)  or  for  yt7  (speed 
deviation).  By  differentiation  of  (2)  with  regard  to  t  and  by 
substitution  from  (1)  we  obtain 

Ta\*d*X       X          dX      Ti  1    dX      Th  d2X 


(¥) 


dt*        T,      *  dt  "  2  T.  dt  '     2     dt2 


The  introduction  of  the  various  time  elements  in  the  theory 
of  governors  is  due  to  Professor  Stodola  (Schweizerische  Bau- 
zeitung,  1893  and  1894). 

To  eliminate   X  and  obtain  an  equation  for  U,  form  the 
derivatives  of  X  from  (1)  and  substitute  in  (2).    We  obtain 

dU      Ti  dU      TbT8  d*U 
-U  -  Tsp-r--  —  — --—-—-=  Q.  .(4) 


8  dt*  al    dt        2    dt          2      dt 


134    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

By  arranging  both  (3)  and  (4)  with  regard  to  the  order  of 
the  derivatives,  we  obtain 


^+?©21f-  +  7^5f?  +  7^*-°-<6> 

j 
and 


,     dU  [/_0        _ 


The  equations  for  £7  and  X  are  identical.    At  first  thought 

this  may  appear  strange,  because  we  know  from  previous  ex- 

.  planation  that  the  curve  of  govern- 

or motion  and  the  curve  of  speed 
of  prime  mover  do  not  coincide. 
However,  this  seeming  discrep- 
ancy will  disappear  shortly. 

Equations  of  the  type  of  (5) 
and  (6)  are  known  in  mathe- 
matics as  linear  differential  equa- 
tions of  the  third  order  with  right- 
hand  member  equal  to  zero.  Their  integral  equations  are  well 
known.  Let  equation  (5)  be  written 

d*X  .dzX  dX 

—  -+#!  —  +  JK2  —  -  +  K3X  =  0  ; 
dts  dt2  dt 

then  the  character  of  the  motion  represented  by  the  equation 
depends  entirely  upon  the  relation  between  the  three  coef- 
ficients KI,  K2,  and  K^  all  of  which  are  built  up  of  time  ele- 
ments, with  the  exception  of  p.  Correct  governing  is  a  game  of 
getting  there  first  with  the  lowest  terminal  velocity.  The  theory 
of  vibrations  teaches  that,  if  the  product  KI  K2  is  greater  than 
K3,  the  governor  comes  to  rest  after  a  change  of  load.  The 
motion  is  then  represented  either  by  Fig.  89  or  Fig.  90.  If 
KI  K2  =  Kz  then  the  motion  is  kept  up  indefinitely  with  con- 
stant amplitude  (limiting  case,  see  Fig.  91).  If  KI  K2  is 
less  than  K3,  the  amplitude  increases  continually. 


INTERACTION    BETWEEN    GOVERNOR   AND    PRIME    MOVER     135 


The  case  of  Fig.  90  is  the  one  most  usually  occurring  in 
practice.     It  is  represented  by  the  equation 

X  (or  U)  =  K*  e^  +  (j£6  sin  z3 1  +K6  cos  z3 1)  e* (7) 

where  e  is  the  basis  of  natural  logarithms,  (2.71828),  and  where 
21,  £2  +  23  V  -  1,  £2  —  £3  V  -  1  are  the  three  roots  of  the  equa- 


U-  Relafive  Speed  Change 


X'Governor  Displacement 


Time 


FIG.  90 


tion  z3  +  Kl  z1  +K2  z  +  K3  =  0.  The  coefficients  K4,  K6  and  K6 
are  to  be  found  from  the  state  of  motion  at  the  instant  when 
the  change  of  load  occurred.  They  differ  in  the  solution  for  X, 
from  those  obtained  in  the  solution  for  C7,  as  will  easily  be  under- 


U-  Relative  Speed  Change 


-Governor  Displacement 


Time 


FIG.  91 


stood  from  a  study  of  Fig.  91.  At  the  beginning  of  a  disturb- 
ance the  velocity  curve  starts  with  a  finite  angle,  whereas  the 
governor  motion  curve  must  start  tangent  to  the  horizontal 
axis.  This  explains  how  the  two  curves  of  U  (velocity)  and  X 


136    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

(governor  displacement)  can  be  quite  different  in  spite  of  having 
the  same  differential  equations.  The  coincidence  of  the  latter 
simply  expresses  that  both  vibrations  are  made  stable  or  un- 
stable by  the  same  combination  of  time  elements,  that  their 
period  of  vibration  is  identical,  that  they  have  the  same  rate 
of  damping,  etc.  Although  the  proof  cannot  be  given  here,  it 
may  be  mentioned  that  (1)  the  period  (or  length  of  each  wave) 
is  always  the  same,  independent  of  the  load  change,  (2)  that 
both  the  speed  fluctuation  and  the  governor  displacement 
(referred  for  instance  to  the  first  wave)  are  directly  propor- 
tional to  the  load  change. 

To  find  this  speed  variation  of  the  first  wave,  the  derivative 
of  equation  (7)  for  U  must  be  equated  to  zero,  that  is  to  say, 

we  must  form  —  =  0  ;  we  must  then  solve  the  resulting  equa- 
dt 

tion  for  t,  which  can  be  done  by  trial  only,  because  t  appears 
both  as  an  exponent  and  as  a  factor  of  an  angle.  The  resulting 
value  of  t  is  substituted  in  equation  (7),  and  U  maximum  is 
found. 

Creative  practice  pays  no  attention  to  these  equations, 
because  they  are  too  complicated.  It  takes  much  longer  to 
master  and  apply  them  than  it  takes  to  build  a  governor  and 
try  it.  Besides,  the  practically  important  features  can  be  ascer- 
tained much  more  easily  from  the  limiting  case.  In  spite  of 
this  condition,  no  apology  is  offered  for  the  introduction  of 
this  brief  sketch  of  the  theory,  because  no  one  can  ever  appre- 
ciate the  great  usefulness  of  the  simple  equations  of  the  limit- 
ing case,  unless  he  has  wrestled  for  days,  or  even  for  weeks, 
with  the  solution  of  the  complete  equation. 

In  the  advanced  volume  a  few  examples  of  the  complete 
calculation  will  be  given  for  the  benefit  of  those  who  wish  to 
make  the  governing  of  prime  movers  a  life  study. 

In  estimating  the  probable  maximum  fluctuation  from  the 
limiting  case,  we  must  take  care  of  the  assumptions  upon 
which  it  is  based.  Referring  to  Fig.  91,  note  that  the  vibra- 
tion is  not  sine  harmonic  at  the  outset,  but  soon  becomes  so. 
Consequently,  the  speed  changes  (1)(2),  (3)  (4),  (5)  (6),  etc., 
are  not  equal  to  one  another.  Definitely  known  from  theory 


INTERACTION    BETWEEN    GOVERNOR   AND   PRIME    MOVER     137 

^| 

are  the  speed  change  (!)(£)  =  -~p,  and  the  amplitude  (7)  (8) 

A-  o 

of  the  sine  harmonic  vibration  which  finally  establishes  itself, 

i  A  T   /T~ 

and  which  equals  -  —  -~  \—     But  what  we  are  desirous  of 

L  A.  o    1  3        p 

knowing  is  the  fluctuation  (1)  (3)  of  Fig.  90.     As  in  Fig.  91,  (1)  (2) 
A 

equals  —  p  in  Fig.  90  also;  but  (#)(#)  is  the  trouble  maker. 
A  o 

A      i    A  T    rr~ 

We  may  replace  (1)  (3)  by  -  -  p  +  -  K  —  — -  •%/ —  where  K  is  a 

^LO        2     ^LO  i  s    v  p 

stop-gap  coefficient,  the  lowest  value  of  which  is  approximately 
1.2,  and  the  average  value  of  which  is  1.6.  K  may  reach  2  or  3, 
if  much  energy  is  stored  up  beyond  control  of  the  governor,  as 
for  instance  in  compound  or  triple-expansion  engines,  or  in 
four-cycle  gas  engines.  In  the  latter  case  it  is  better  to  use  the 
average  coefficient  1.6  and  to  add  separately  the  speed  change 
caused  by  the  stored-up  energy.  Then  we  have 

du                                         A               A     Tg    7l        E 
-  =  (approximately)  U  =  -j-p  +  .8  —  —  y—  +77^ (8) 

U  -£>-  o  ilo-LapJ-U 

where  E  is  the  available  stored-up  energy,  I  the  moment  of 
inertia  of  the  rotating  parts,  and  u  the  average  angular  velocity. 
In  a  tandem  double-acting  four-cycle  gas  engine,  E,  for  a 
sudden  change  from  full  load  to  no  load  equals  twice  the  maxi- 
mum work  done  by  each  cylinder  per  power  stroke,  because 
one  cylinder  carries  a  compressed  rich  charge  and  another 
cylinder  has  taken  in  a  full  charge  of  rich  mixture.  Both  of 
these  charges  will  do  maximum  work,  no  matter  what  the 
governor  does.  If  there  is  a  large  amount  of  explosive  mixture 
stored  between  the  governor  valve  and  the  cylinder,  matters 
are  worse. 

Since  the  steam  turbine  is  to-day  the  principal  prime  mover, 
a  brief  sketch  of  a  method  of  computing  the  speed  rise  due  to 
energy  beyond  control  of  the  governor  will  be  appropriate.  In 
a  steam  turbine  both  the  steam  in  the  steam  chest,  W8  (pounds), 
and  the  steam  in  the  turbine,  Wt,  will  do  work  after  the  closing 
of  the  governor  valve.  This  work  is  passed  on  to  the  turbine 
with  an  efficiency  e.  Let  EI  be  the  Rankine  cycle  work  of  a  pound 


138    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

of  steam  between  inital  and  exhaust  conditions  (which  work 
can  be  found  from  a  total  heat-entropy  chart),  then  the  work 
done  by  the  steam  not  under  governor  control  equals 

E  =  (W8  +  i  Wt)e  E,. 

Not  all  of  Wa  does  work,  because  a  small  amount  remains 
at  the  end  of  the  expansion;  however,  it  can  be  neglected. 
Only  one  half  of  Wt  is  put  into  the  equation,  because  the 
steam  in  the  turbine  has  only  about  half  as  much  available 
energy  per  pound  as  that  in  the  chest,  e  is  A  for  very  small 
turbines,  .65  for  the  largest  turbines. 


,  Du 

The  relative  speed  rise  is  -  -  =  U  =  -  ^  — 

u  I  u 

The  numerical  addition  of  the  three  items  in  speed  rise, 
namely  static  speed  rise,  dynamic  speed  rise  under  control  of 
the  governor,  and  dynamic  speed  rise  beyond  control  of  the 
governor  is  an  approximation  only.  The  true  calculation  is 
hopeless,  as  before  mentioned.  If,  for  any  reason,  the  exact 
knowledge  of  the  greatest  speed  fluctuation  should  be  desired, 
a  point  by  point  method  may  be  used.  (See  83,  Ruelf,  Der 
Reguliervorgang  bei  Dampfmaschinen,  and  34,  Koob,  Das 
Regulierproblem  in  vorwiegend  graphischer  Behandlung.) 

References  to  Bibliography  at  end  of  book:   15,  18,  32,  34,  36,  57,  65,  73,  83. 


CHAPTER  X 

DISCARDED  TYPES  OF  SPEED  GOVERNORS 

THE  speed  governors  which  were  discussed  and  the  theory 
of  which  was  developed  up  to  this  point  are  based  on  "  Watt's 
principle,"  which  means  that  the  centrifugal  force  of  revolving 
masses  is  opposed  by  a  centripetal  force,  and  that  any  differ- 
ence between  the  two  constitutes  the  motive  force  of  the 
governor.  The  inertia  governors  treated  in  paragraphs  2  of 
Chapter  II  and  3  of  Chapter  IX  are  seemingly  an  exception 
to  this  statement;  in  reality  they  are  not,  because  they  are 
useful  only  on  condition  that  tangential  inertia  is  coupled 
with  centrifugal  force. 

At  first  thought,  Watt's  principle  seems  to  be  very  unsatis- 
factory, because  a  change  of  speed  (which  the  governor  is 
intended  to  prevent)  must  occur  before  the  governor  can  act. 
It  is,  therefore,  quite  natural  that  inventors  of  many  countries 
should  have  worked  hard  to  design  governors  on  the  basis  of 
apparently  more  promising  principles.  However,  the  governors 
based  on  Watt's  principle  have  survived,  while  governors  based 
on  other  principles  have  disappeared. 

Nevertheless,  knowledge  of  the  discarded  principles  is 
valuable,  particularly  if  it  is  coupled  with  knowledge  of  the 
reasons  why  they  failed  to  meet  the  requirements  of  practice. 
For  only  by  such  knowledge  can  people  with  inventive  minds 
be  prevented  from  reinventing,  with  the  courage  of  ignorance, 
mechanisms  which  were  relegated  to  the  scrap  heap  long  ago. 

Tangential  Inertia 

The  principle  of  using  tangential  inertia  for  governing  was 
investigated  in  paragraph  2  of  Chapter  II.  It  suffices  here  to 
refer  to  that  paragraph.  The  general  idea  of  using  tangential 
inertia  was  first  published  by  Werner  and  William  Siemens  in 

139 


140    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


1845.  Hence  it  is  known  as  "  Siemens'  principle."  It  is  c.learly 
illustrated  by  Fig.  92.  The  inertia  mass  (1)  tends  to  maintain 
a  constant  speed,  no  matter  what  the  latter  may  be.  To  keep 

Power  Control 
Mechanism 


pinion  rotates  continually 
FIG.  92 

wheels  (1)  and  (2)  from  losing  speed  and  running  down,  shaft 
(4)  must  drive  shaft  (6)  by  means  of  sufficient  friction.  Any 
acceleration  or  retardation  of  shaft  (4)  causes  the  supporting 

load 


Power  conio! 
nism 

.-4  4J  f   W — *-4 

Spring 


Prime 
Mover 


FIG.  93 


axle  of  planetary  gear   (5)  to  rotate  about  point   (3),  which 
motion  is  utilized  to  adjust  the  energy  control  mechanism. 

The  reasons  why  Siemens'  principle,  by  itself,  cannot  be 
used  for  governing  were  explained  in  paragraph  2  of  Chapter  II. 


DISCARDED  TYPES  OF  SPEED  GOVERNORS 


141 


Dynamometric  (or  Load-)  Governors 

Poncelet,  in  1829,  proposed  a  governing  principle  which  is 
illustrated  by  Fig.  93.  The  torque  from  prime  mover  to  load 
passes  through  a  flexible  spring  coupling.  The  twist  causes 
gears  (1)  and  (5)  to  be  displaced  with  regard  to  each  other. 
Hence  gears  (2)  and  (4)  (in  mesh  with  (1)  and  (5))  are  also 
displaced,  which  causes  gear  (2)  to  travel  along  screw  (3). 
Axial  displacement  of  (2)  shifts  power  control  mechanism. 


Power  Control 
Mechanism 


Seeming  advantage: 
The  action  is  practically 
instantaneous  as  soon  as 
load  changes. 

Drawback :  The  feature 
which  makes  this  governor 
impossible  is  its  failure  to 
adjust  the  power-control 
mechanism,  if  intensity  of 
available  energy  varies  (for 
instance  steam  pressure, 
back  pressure,  head  of 
water  in  hydraulic  tur- 
bines, etc.).  It  has  other 
drawbacks,  namely  vibra- 
tions due  to  flexible  couplings,  and  never-ending  vibrations  in 
case  the  load  changes  suddenly  (no  damping).  It  does  not 
maintain  a  constant  speed. 


FIG.  94 


Chronometric  Governors 

If  the  flywheel  of  Fig.  92  is  replaced  by  a  time-piece,  which 
maintains  a  uniform  speed  of  bevel  gear  (#),  then  the  governor 
is  called  a  "  chronometric  governor."  This  type  was  invented 
by  Sir  C.  W.  Siemens  in  1843.  One  of  the  many  possible  forms 
is  shown  in  Fig.  94.  Bevel  gear  and  spindle  (3)  are  driven  by 
the  prime  mover.  Planetary  gear  (2)  drives  the  time-piece  (6) 
through  bevel  gear  (1),  and  operates  the  power-control  mecha- 
nism through  segment  (5)  and  gear  (4).  The  latter  pair  does 


142    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


not  revolve  continually,  but  moves  only  to  adjust  the  position 
of  the  power-control  mechanism. 

In  the  mechanism  shown  in  the  illustration,  the  uniform 
speed  of  (6')  and  (1)  is  obtained  by  the  friction  brake  (7), 
which,  if  desired,  may  be  replaced  by  an  oil  brake.  If  the 
weights  (6)  go  faster  than  desired,  the  friction  force  is  greater, 
so  that  their  speed  is  reduced.  If  they  go  slower  than  desired, 

the  friction  is  reduced,  so 
that  the  driving  mecha- 
nism can  speed  them  up. 
Compared  to  the 
purely  centrifugal  gov- 
ernor, the  chronometric 
governor  possesses 
several  disadvantages. 
First,  the  friction  brake 
consumes  power,  or,  if  an 
independent  source  of 
energy  is  employed  for 


fime- 


the  time-piece,  its  energy 
is  wasted,  in  addition  to 
FIG.  95  the  disadvantage  of 

requiring  attention. 

Second,  a  "jack  in  the  box"  gear  is  an  unwelcome  com- 
plication. 

Third,  sudden  changes  of  load  produce  never-ending  speed 
fluctuations.  Let  part  of  the  load  suddenly  be  removed  at 
points  (1)  and  (11),  Fig.  95;  then  gear  wheel  (3)  of  Fig.  94 
will  go  ahead  of  wheel  (1).  At  points  (2)  and  (12)  of  Fig.  95, 

du 

torque  equilibrium  exists,  and  —  =  0;   but  wheel  (3),  Fig.  94, 

at 

still  runs  ahead  (see  excess  speed  (2)  (3),  Fig.  95),  so  that  the 
governor  travels  too  far,  namely  to  point  (13)  instead  of  point 
(12).  The  governor  oscillates  about  its  new  position,  and  the 
speed  of  the  prime  mover  oscillates  about  the  "  synchronous 
speed."  The  three  disadvantages  taken  together  have  made 
it  impossible  for  the  chronometric  governor  to  compete  with 
the  high-grade  centrifugal  governor. 


DISCARDED  TYPES  OF   SPEED  GOVERNORS 


143 


Cataract  Governors 

(Also  known  as  pump  governors,  hydraulic  governors, 
atmospheric  governors  or  pneumatic  governors) 

The  principle  of  this  method  of  regulation  is  clear  from 
Fig.  96.  A  pump  (1)  driven  by  the  prime  mover  delivers  fluid 
to  a  receptacle  (3),  from  which  it  returns  to  the  pump  through 
an  orifice  (#),  which  is  usually  made  adjustable.  The  depth 
of  the  liquid  in  the  upper  receptacle  (respectively  the  pressure, 
if  the  fluid  be  a  gas),  regulates  the  supply  of  energy  to  the 


Power 

Control 

Mechanism 


FIG.  96 

prime  mover.  In  the  illustration,  the  float  (4)  operates  the 
power-control  mechanism. 

The  cataract  principle  antedates  the  centrifugal  governor 
of  James  Watt.  It  was  used  on  the  Cornish  pumping  engines. 
It  can  be  used  to-day  to  govern  the  number  of  strokes  per 
minute  of  direct-acting  pumps  and  compressors  (which,  as  is 
well  known,  have  neither  crank  nor  flywheel). 

For  turbines,  and  for  engines  with  flywheels,  the  cataract 
principle  has  been  very  little  used.  The  principal  drawback 
is  variation  of  viscosity  (and  of  density)  of  the  working  fluid  in 
the  governor.  If  the  type  in  question  is  to  be  used  for  engines 
or  turbines,  centrifugal  pumps  or  rotary  pumps  are  preferable 
to  reciprocating  pumps. 


144    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

With  proper  design,  the  principle  is  capable  of  development, 
for  special  purposes  of  regulation,  particularly  in  connection 
with  direct-acting  pumps. 

Vane  Governors 

The  resistance  which  a  fluid  offers  to  revolving  vanes  has 
been  used  as  a  principle  upon  which  to  design  governors  for 
prime  movers.  Figure  97  illustrates  this  type.  Vanes  (1)  in 
box  (2)  are  driven  by  the  prime  mover.  The  liquid  which  partly 
fills  the  box  is  taken  along  by  the  vanes  with  a  fraction  of  their 
angular  velocity.  The  moving  liquid  exerts  a  drag  on  the 


Power  Control 
Mechanism 


Driven 
prime  mover 

FIG.  97 


Fixed 


casing  (which  is  provided  with  many  projections  for  that  pur- 
pose). The  drag  is  resisted  either  by  a  spring  or  by  a  weight- 
Governors  designed  on  this  principle  bear  different  names 
(derived  from  the  names  of  their  inventors)  in  different  coun- 
tries. They  always  involve  a  loss  of  energy.  Besides,  the  dissi- 
pated energy  is  converted  into  heat,  which  changes  the  density 
and  viscosity  of  the  oil  (or  other  fluid)  and  with  them  the 
equilibrium  speed  of  the  governor.  The  principle  has  been 
abandoned  and  is  not  likely  to  be  introduced  again. 

Centrifugal  Compensator 

Recognition  of  the  reasons  why  an  isochronous  governor 
fails  to  produce  isochronous  governing  led  Knowles  in  1884  to 


DISCARDED   TYPES   OF  SPEED   GOVERNORS 


145 


the  invention  of  a  practical  solution,  the  principle  of  which  is 
illustrated  in  Fig.  98.  Knowles'  principle  has  been  discarded, 
not  because  it  is  impracticable,  but  because  the  same  end  can 
be  attained  by  much  simpler  means  (see  paragraph  2  of  Chapter 
IX).  In  the  illustration,  (1)  is  a  centrifugal  governor  with 
sufficient  static  fluctuation  to  insure  stability  of  regulation  ; 
(6)  is  a  similar  governor,  the  regulating  travel  of  which  is  kept 
within  narrow  limits.  (1)  is  the  main  governor,  (6)  is  the 
auxiliary  governor.  From 
previous  explanations  it 
is  known  that  different 
speeds  belong  to  the  posi- 
tions (2)  (3)  (4)  of  gover- 
nor (1 ) ,  and  would  likewise 
belong  to  positions  (10) 
(9)  (8)  of  the  power- 
control  mechanism,  if  the 
length  of  the  link  (3)  (9) 
remained  constant.  If, 
however,  after  a  change 
of  load,  governor  (1),  and 
with  it  the  upper  end  of 
link  (3)  (9),  is  returned  to 
one  and  the  same  position, 

then  one  and  the  same  speed  corresponds  to  all  positions  of 
the  power-control  mechanism.  This  desirable  object  is  gained 
by  making  link  (3)  (9)  adjustable  in  length  and  by  automatically 
returning  governor  (1)  to  the  same  position.  The  auxiliary 
governor  (6),  by  means  of  friction  wheel  (5),  pulleys  (7),  and 
turnbuckle  (11),  slowly  adjusts  the  length  of  link  (3)  (9).  Equili- 
brium obtains  if  the  speed  of  the  prime  mover  keeps  the  auxiliary 
governor  free  from  the  friction  wheel.  The  equilibrium  speed 
of  governor  (6*)  should  coincide  with  the  mid-position  speed  of 
governor  (1). 

Governor  (6)  takes  the  place  of  the  compensating  oil  pots 
explained  in  Chapters  IX  and  XIII ;  so  that  it  may  be  called 
a  centrifugal  compensator. 

While  Knowles'  principle  has  been  discarded  in  direct-con- 


Power  Control 
Mechanism 


146    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

trol  governing,  a  modified  form,  with  one  governor  only,  is 
extensively  used  in  relay  governing  (see  Fig.  123). 

Electrical  Governors 

At  the  present  time  power  is  transmitted  long  distances 
almost  exclusively  by  electrical  means,  so  that  prime  movers 
for  power  generation  and  transmission  (as  distinguished  from 
prime  movers  for  pumping,  blowing,  etc.)  are  used  more  and 
more  for  driving  electric  generators  to  the  gradual  exclusion  of 
everything  else. 

Electrical  energy  is  quick  acting  and  is  free  from  mechanical 
friction.  It  lends  itself  beautifully  to  the  design  of  regulators 
and  governors.  In  consequence,  many  attempts  have  been 

made  to  use  electricity  directly  for¥ 
governing,   and  to  circumvent  the 
Ffxed  comparatively  slow  mechanical 
governor. 

The  principle  of  an  electrical  type 
of  governor  which  was  in  use  for 
more  than  a  decade  will  be  under- 
stood from  Fig.  99.  Core  (4)  and 
coil  (5)  form  a  solenoid,  the  attrac- 
tion of  which  is  counteracted  by  a 
spring  (1).  If  the  current  in  (5)  is 
increased,  core  (4)  is  pulled  down, 
and  the  throttle  valve  (2)  moves 
toward  closed  position.  In  practice, 
the  travel  of  the  core  must  be  kept 
very  small,  to  avoid  hunting.  The  use  of  an  oil  gag  pot  (8) 
reduces  hunting,  but  does  not  eliminate  it.  To  keep  the  travel 
of  (4)  small,  a  relay  was  interposed  in  practice  (see  Chapter  XIII). 
The  governor  in  question  was  used  mainly  on  constant 
(direct)  current  arc  lighting  machines.  Maintaining  constant 
current  meant  great  variation  in  speed,  depending  upon  the 
number  of  lamps  in  the  circuit,  and  for  that  purpose  the  governor 
was  well  suited.  Direct  current  arc  lighting  for  streets  is  to-day 
a  matter  of  past  history.  When  the  direct  current  arc  lighting 
machine  went  out  of  usage,  the  governor,  Fig.  99,  went  with  it. 


•JE 


1 


FIG.  99 


DISCARDED   TYPES   OF  SPEED   GOVERNORS  147 

In  alternating  current  work,  it  is  desirable  to  maintain  a  given 
number  of  cycles,  and  to  govern  voltage  by  electrical  means. 
But  a  constant  number  of  cycles  means  a  constant  speed  of 
the  prime  mover,  and  for  that  purpose  the  revolution  counter, 
or,  in  other  words,  the  centrifugal  governor,  is  the  best  solution. 
If  maintaining  a  constant  voltage,  without  any  regard  to  the 
number  of  cycles,  were  the  prime  consideration,  then  and  in 
that  case  it  is  highly  probable  that  governing  would  be  accom- 
plished to-day  by  electrical  means. 

References  to  Bibliography  at  end  of  book:  4,  5,  6,  22,  31,  36,  39,  42,  61,  62,  80. 


CHAPTER  XI 

GOVERNING  FOR  CONSTANT  RATE  OF  FLOW 

IN  connection  with  prime  movers  driving  pumps,  cases  are 
encountered  in  which  it  is  necessary  to  keep  the  rate  of  delivery 
of  the  pump  constant.  The  type  of  governor  employed  for 
this  purpose  varies  with  the  type  of  pump. 

In   positive   displacement   pumps    (including   reciprocating 
and  rotary  blowers),  the  delivery  is,  within  reasonable  limits, 
proportional  to  the  angular  velocity,  and  independent  of  the 
resistance  to  flow  on  the  discharge  side.     Consequently,  con- 
stant delivery  is,  within  the  same  limits,  identical  with  constant 
speed,  and  prime  movers  driving  constant  displacement  pumps 
or  blowers  are,   for  the  purpose  in  question,   equipped  with 
constant  speed  governors.     If  the  resistance  to   flow  varies 
widely,    constant    speed    does    not    mean    constant    delivery, 
because  the  volumetric  or  delivery  efficiency  drops  in  all  posi- 
tive displacement  machines,  as  the  resistance  is  increased.    The 
reduction  of  volumetric   efficiency  is   due    to    several    causes 
such  as  leakage  and   slip,   reexpansion    in    clearance  volume, 
heating  of  incoming  gas,  reevaporation  (if  vapor  is  pumped) 
etc.,  which  need  not  be  discussed  here.     Since  increased  re- 
sistance means  increased  pressure  on  the   delivery  side,   the 
reduction  of  volumetric  efficiency  can  automatically  be  com- 
pensated for  by  a  slowly  applied  increase  of  speed  under  the 
influence  of  increased  pressure.     (In  the  case  of  vacuum  pumps, 
substitute  " suction  side"  and  " decrease  of  pressure"  for  " dis- 
charge side  "  and  "  increase  of  pressure.")     There  should  be 
no  difficulty  in  accomplishing  this  result,  although  no  applica- 
tions of  this  thought  appear  in  practice. 

Matters  are  quite  different  with  velocity  pumps,  of  which 
type  the  centrifugal  pump  and  the  turbo-blower  are  repre- 
sentatives. The  rate  of  delivery  is  a  function  of  both  angular 

148 


RATE-OF-FLOW  GOVERNORS 


149 


velocity  and  resistance  to  flow,  so  that,  for  a  given  speed,  the 
flow  may  vary  within  wide  limits.  Speed  governors,  therefore, 
will  not  do  for  maintaining  constant  rate  of  flow,  but  a  force 
must  be  derived  from  the  flow  itself.  Here  a  wide  field  is  open 
to  the  ingenuity  of  inventors,  because  there  exist  so  many 
methods  for  deriving  a  force  from  the  rate  of  flow.  If  we  glance 
over  the  variety  of  centrifugal  governors  and  remember  that 
they  are  all  based  upon  one  single  force  action,  namely  that  of 
centrifugal  force,  then  we  begin  to  realize  what  a  number  of 
"  constant  volume"  governors  is  possible  using  either  the  im- 
pact disk,  or  the  Venturimeter,  or  the  Pitotmeter  or  nozzles 
-and  orifices,  or  constant  pressure  difference  with  variable 
orifice  area,  or  temperature  rise  methods,  etc.  With  all  this 
variety  of  possibilities  there  is  a  certain  similarity  between 
volume  governing  and  speed  governing,  as  will  be  apparent 
from  the  following  : 

In  centrifugal  pumps  and  low  pressure  turbo-blowers  the 
relation  between  angular  velocity  u,  pressure  p  and  rate  of 
delivery  V  is  (near  enough  for  all  practical  purposes)  given  by 
the  equation 

p  = 


s- 

D 
1/5 
l/> 

OJ 
i_ 
d. 

o: 


where  Ki  and  K2  are  design  constants  peculiar  to  each  machine,1 

see  also  Fig.  100.     If  now  the  pump  or  blower  operates  solely 

against  a  friction  resistance 

(centrifugal  pumps  in  closed 

systems,  blowers  for  fur- 

naces, etc.),  the  pressure 

generated  by  the   pump   is 

used  for  overcoming  friction 

resistance  only,  which  may 

be  expressed  by  the  equation 

p  =  K,V\      (In  high  lift 

centrifugal  pumps  this  rela- 


Resistance 
Characteristic 


Pump 
Characteristic 


V-  Rate  of  Del  ivery 
FIG.  100 


tion  does  not  hold.    For  such 

pumps,  however,  volume  governing  is  practically  never  used.) 

1  This  equation  does  not  apply  to  turbo-compressors,  on  account  of  the  change 
of  density  with  pressure.  But  turbo-compressors  are  governed  for  constant  pres- 
sure, and  not  for  constant  volume.  Therefore,  the  discrepancy  does  not  matter. 


150    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

Combining  the  two  equations  furnishes  (Kz  +  K2)V2  =  K:u2  or 
finally  _ 

^~  ...............  (1) 


Evidently  the  rate  of  delivery  is  directly  proportional  to  the 
speed,  as  long  as  the  external  resistance  Kz  remains  constant. 
But  the  latter  is  usually  the  case.  If,  for  instance,  a  turbo- 
blower delivers  air  to  a  blast  furnace,  the  changes  of  resistance 
in  the  furnace,  although  of  considerable  magnitude,  occur  so 
slowly  that  during  the  period  of  one  process  of  regulation 
(caused,  for  instance,  by  a  sudden  change  of  steam  pressure), 
the  resistance  may  be  considered  constant.  But  if  relation 
(1)  holds,  all  the  theories  applying  to  speed  governing  must 
also  apply  to  volume  governing.  There  must  be  a  static  fluc- 
tuation (difference  of  pressure  between  great  and  small  resist- 
ance), there  exists  a  limiting  case  of  never-ending  vibrations, 
a  gag  pot  is  needed  to  enforce  stability,  etc.  For  this  reason 
it  is  unnecessary  to  go  further  into  the  theory  of  volume  govern- 
ing, because  the  theory  of  speed  governing  can  be  applied  with 
small  changes. 

The  two  types  of  "  volume"  governors  which  are  at  the 
present  time  in  use  in  the  United  States  are  diagrammatically 
illustrated  in  Figs.  101  and  102.  In  both  illustrations  the 
force  derived  from  the  rate  of  flow  is  shown  as  operating  the 
energy-controlling  device  directly,  whereas,  in  practice,  a  relay 
is  used.  The  latter  part  of  the  governors  will  be  found  discussed 
in  Chapter  XIII. 

In  Fig.  101  (General  Electric)  an  impact  disk  is  used.  The 
disk  produces  a  pressure  difference  due  to  throttling  and,  at 
the  same  time,  acts  as  piston  for  converting  the  pressure  differ- 
ence into  a  regulating  force.  In  Fig.  102  (Rateau,  Ingersoll- 
Rand)  a  partial  vacuum  is  produced  by  a  Rateau  multiplier  (two 
or  three  Venturi  tubes  in  a  set).  The  suction  is  transmitted  to 
a  separate  piston  (4). 

Many  of  the  definitions  from  the  statics  of  centrifugal 
governors  can  be  applied  here,  if  properly  modified.  In  both 
types  the  "  strength"  of  the  governor  is  found  by  the  force 


RATE-OF-FLOW  GOVERNORS 


151 


which  is  required  to  move  the  governor  when  it  is  not  in  opera- 
tion, which  in  the  present  case  means  without  flow.  The  whole 
strength  cannot  be  utilized  in  regulation,  because  that  would 
require  cessation  of  flow.  The  governor  has  a  work  capacity 
depending  upon  the  governor  piston  displacement  and  upon 
the  pressure  difference  due  to  the  allowable  difference  in  the 
rate  of  flow.  Both  governors  have  stability  and  a  static  fluc- 
tuation. In  Fig.  101  stability  is  obtained  by  cone  angle  i  and 
the  spring  (1).  In  Fig.  102  it  is  obtained  by  the  spring  (1). 
If  the  steam  pressure  varies,  or  the  resistance  of  the  furnace 
varies,  the  control  valve  (2)  must  change  its  position,  which 


Fulcrum 


Partial    Vacuum 


Steam 
Line 


CD 


FIG.  101 


FIG.  102 


(on  account  of  the  just  mentioned  stability)  means  that  the 
rate  of  flow  must  change.  If  the  stability  is  too  small,  that  is 
to  say  if  it  is  attempted  to  regulate  too  closely,  never-ending 
vibrations  will  result ;  the  governor  will  hunt,  unless  special 
gag  pots,  etc.,  are  used  (see  paragraph  2  of  Chapter  IX). 

Just  as  in  speed  governors  adjustment  of  speed  is  obtained 
by  variation  of  strength,  so  in  volume  governors  adjustment  of 
rate  of  flow  is  obtained  by  the  same  means.  In  Fig.  101  the 
strength  is  varied  by  the  shifting  of  the  weight  (3)  along  its 
supporting  lever,  and  in  Fig.  102  the  same  is  accomplished  by 
turning  hand  wheel  (3),  which  varies  the  initial  compression  of 
spring  (1). 


152    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

The  complete  theories  of  these  two  governors,  including  the 
measuring  apparatus  for  the  rate  of  flow,  are  not  difficult.  But 
they  will  not  be  given  here,  because  the  governors  are  patented, 
which  means  that  the  theory  would  benefit  only  a  very  limited 
circle  of  engineers. 

In  connection  with  volume  governors  it  should  be  remarked 
that  frequently  more  is  expected  of  them  than  they  can  accom- 
plish. This  refers  particularly  to  the  application  of  such  gov- 
ernors to  blast  furnace  blowing  equipment.  In  blast  furnace 
practice  the  furnace,  the  boilers  and  the  blowers  are  interde- 
pendent. If  the  furnace  hangs  (resistance  becomes  very  great), 
more  steam  is  used,  while  the  gas  supply  from  the  furnace  to 
the  boilers  remains  constant.  The  steam  pressure  drops,  so 
that  still  more  steam  is  used.  Soon  a  limit  is  reached,  and  the 
rate  of  flow  of  air  to  the  furnace  cannot  be  maintained,  unless 
the  heat  input  into  the  boilers  is  increased  by  other  means, 
such  as  coal  fire.  If  the  quantity  of  blast  falls  off,  the  supply 
of  gas  also  falls  off,  the  steam  pressure  is  lowered  still  more, 
etc.  Most  obviously  neither  a  constant  volume  governor  on 
a  turbo-blower  nor  a  constant  speed  governor  on  a  reciprocating 
blower  can  obviate  or  cure  such  a  condition,  and  should  never 
be  expected  to  do  so. 

Reference  to  Bibliography  at  end  of  book:  81. 


CHAPTER  XII 

GOVERNING  FOR  CONSTANT  PRESSURE 

IN  the  governing  of  pumping  machinery,  the  most  widespread 
requirement  of  regulation  is  to  keep  constant  the  pressure  (or 
suction)  produced  by  the  pump,  no  matter  how  much  the 
demand  or  rate  of  flow  of  fluid  pumped  may  vary. 

Pressure  governing  differs  from  speed  governing  in  many 
respects.  Although  the  reasons  for  the  differences  will  not 
appear  until  later  in  the  chapter,  the  principal  differences  will 
be  mentioned  here  for  the  sake  of  greater  clearness.  First, 
the  influence  of  pressure  governing  upon  the  prime  mover  is 
felt  more  slowly  than  that  of  speed  governing,  because  change 
of  pressure  is  the  accumulated  effect  of  speed  deviation.  Second, 
different  pumps  have  widely  varying  characteristics  (relations 
between  pressure,  rate  of  flow  and  speed),  so  that  a  governing 
device  which  is  successful  with  one  type  of  pump  may  be  a 
failure  with  another  type  of  pump.  Third,  while  in  speed 
governing  the  two  variables,  namely  torque  and  angular  ve- 
locity, are,  within  reasonable  limits,  independent  of  each 
other,  the  variables  in  pressure  governing  are  not  independent 
of  each  other  ;  the  resisting  torque  (average  per  revolution) 
of  a  pump  is  a  function  both  of  the  pressure  and  of  the  rate  of 
flow.  Finally,  the  word  "regulation,"  when  applied  to  govern- 
ing for  constant  pressure,  is  very  elastic.  While  in  air  com- 
pressor plants  for  mines  and  factories  variations  in  pressure 
of  15%  to  20%  or  even  more  are  allowed,  and  are  considered 
"  close  enough,"  pressure  fluctuations  on  the  suction  side  of 
gas  exhausters  for  by-product  coke  ovens  must  be  kept  down 
to  1/10%  of  the  prevailing  pressure,  and  even  that  small  varia- 
tion is  called  "not  close  enough." 

The  understanding  of  the  phenomena  of  pressure  regulation 
presupposes  familiarity  with  the  characteristics  of  different 

153 


154    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


Atmospheric  Pressure 


FIG.  103 


types  of  pumps.    For  that  reason,  a  brief  discussion  of  the  most 
important  features  of  pump  characteristics  will  now  be  given. 

The  two  types  of  pumps  on  which  pressure  regulation  is 
practiced  are  the  displacement  type  and  the  velocity  type. 
Figures  103  and  104  are  indicator  cards  of  a  water  pump  and 
of  an  air  compressor,  both  of  which  are  dis- 
placement pumps.  The  section  lined  areas 
indicate  losses  due  to  friction  through  valves 
and  ports.  These  losses  increase  with  the 
speed,  so  that  displacement  pumps  have  an 
automatic  stability.  If  the  prime  mover 
delivers  a  given  amount  of  work  per  revolu- 
tion, and  if  the  demand  upon  the  pump 
remains  constant,  the  speed  will  not  increase,  for  two  reasons  : 
First  (if  the  demand  remains  constant),  the  pressure  produced 
by  the  pump  would  rise  with  speed,  and  second,  the  friction 
losses  would  increase  with  speed.  But  both  of  these  mean 
more  work  per  revolution,  which  excess  work  the  prime  mover, 
under  the  assumed  conditions,  is  unable  to  give.  In  some  air 
and  gas  compressors  the  just  mentioned  stability  is  very  small 
or  even  zero.  By  study  of  the  dotted  line  in  Fig.  104,  it  is  easily 
seen  that,  while  the  friction  work 
below  the  atmosphere  increases, 
the  work  of  compression  above  the 
atmosphere  falls  off,  on  account 
of  the  reduced  delivery,  which 
latter  is  occasioned  by  the  pres- 
sure drop  through  the  inlet  valve 
and  ports.  The  stability  is  nega- 
tive in  certain  compression  ranges  i 
of  vacuum  pumps  and  compressors  ™ 
with  fixed  discharge  pressure,  but 
variable  intake  pressure.  It  is  well  known  that  such  pumps 
require  maximum  work  per  stroke,  if  the  intake  pressure  equals 
one  third  of  the  discharge  pressure  (see  Fig.  105).  Below  that 
intake  pressure,  more  speed  means  reduced  intake  pressure,  less 
work  per  stroke  ;  this  in  turn  means  still  more  speed,  etc.  The 
system  is  naturally  unstable.  Fortunately,  close  governing  for 


FIG.  104 


PRESSURE  GOVERNORS 


155 


FIG.  105 


constant  discharge  pressure  is  never  required  with  this  wide  range 
of  intake  pressure. 

The  prime  mover  also  contributes  to  stability  or  lack  of 
stability.  Although  study  of  this  problem  rightfully  belongs 
in  the  chapter  on  the  self-regulating 
properties  of  prime  movers,  it  will  be 
taken  up  here,  as  far  as  it  concerns 
pumping  machinery.  The  prime 
movers  driving  displacement  pumps 
are  steam  engines  and  internal  com- 
bustion engines.  Only  very  occa- 
sionally steam  or  hydraulic  turbines 
are  used.  In  steam  engines,  control 
is  effected  either  by  throttling  or  by 
variation  of  cut-off.  In  throttle 
control,  there  belongs  a  certain  posi- 
tion of  the  throttle  to  a  given  speed  and  pressure  drop.  If  the 
engine  speeds  up  with  a  fixed  position  of  the  throttle,  the  pressure 
drop  through  the  valve  increases,  the  work  done  per  revolution  is 
decreased,  the  deficiency  of  work  is  taken  out  of  the  flywheel, 
and  the  speed  is  reduced  again.  Hence  throttle  control  results 
in  inherent  stability.  It  is  quite  different  with  cut-off  control, 
because  one  and  the  same  position  answers  for  all  speeds  and 
rates  of  delivery  as  long  as  steam-  and  back-pressure  remain 
constant.  In  practice,  this  holds  true  within  certain  limits 
only,  because  there  is  always  some  throttling  in  the  ports, 
which  makes  itself  felt  more  and  more  at  higher  and  higher 
speeds.  But  the  effect  of  speed  is  small,  so  small  as  to  give  very 
little  inherent  stability.  The  latter  must  be  enforced  by  the 
proper  regulating  mechanisms  which  are  described  in  the 
second  paragraph  of  this  chapter. 

The  characteristic  properties  of  pumps  are  expressed  in 
characteristic  curves.  For  displacement  pumps  such  "  charac- 
teristics "  are  not  in  common  use,  because  the  ideal  character- 
istic of  a  displacement  machine  is  a  vertical  straight  line,  see 
Fig.  106,  which  means  that  the  rate  of  delivery  does  not  depend 
upon  the  pressure.  (Fig.  106  is  drawn  for  variable  discharge 
pressure  and  for  constant  suction  pressure.)  Actually,  several 


Discharge  Pressure 

* 

V 

°C 

^ 

\ 

Actual  charac' 

_J 

Ideal  charcict« 

Volume  or  weight  taken  ir> 

FIG.  106 


156    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

circumstances,  depending  upon  the  type  of  pump  and  upon  the 
fluid  pumped,  change  the  shape  of  the  characteristic.  Such 
circumstances  are  slip,  reexpansion  in  clearance  space,  heating 
of  incoming  air  or  gas,  etc.  But  even  with  consideration  of 
these  features,  the  characteristics  of  displacement  pumps  are 
almost  vertical  within  the  practical  range.  Three  character- 
istics are  shown,  namely  for  unit 
or  normal  speed,  for  \  speed  and 
for  double  speed.  For  a  given 
discharge  pressure,  the  delivery  is 
almost  proportional  to  the  speed. 
As  a  rule,  the  delivery  does  not 
grow  as  rapidly  as  the  speed,  partic- 
ularly in  air  and  gas  compressors 
(see  Fig.  104),  unless  an  intake 
pipe  is  provided  of  sufficient  length 
to  use  the  inertia  of  the  fluid  in  it  for  shoving  an  extra  quantity 
into  the  pump  at  the  end  of  the  retardation  period  (end  of  the 
stroke  in  reciprocating  machines). 

Turbo-pumps  and  turbo-compressors  have  no  "  indicator 
cards,"  so  that  the  features  affecting  regulation  must  be  studied 
directly  from  the  pump  characteristics.  While  the  character- 
istics of  centrifugal  (or  turbo-)  pumps  for  liquids  differ  from 
those  of  turbo-compressors,  they  will  not  be  studied  separately 
in  this  sketch,  because  governing  for  constant  pressure  is  not 
common  in  connection  with  centrifugal  pumps,  whereas  it  is 
quite  common  with  turbo-compressors.  In  this  latter  type  of 
turbo-machine  speed,  torque,  pressure,  and  rate  of  delivery 
cannot  be  related  by  any  rational  algebraic  formula,  because 
the  characteristics  vary  greatly  with  the  design  of  the  blades, 
of  the  diffusor,  with  the  rate  of  cooling  between  the  stages, 
with  the  quantity  of  air  slipping  back  per  stage,  and  with 
other  details.  But  in  spite  of  this  variety  there  is  sufficient 
similarity  between  the  characteristics  to  allow  the  drawing  of 
conclusions  for  pressure  regulation.  In  Fig.  107  the  charac- 
teristics of  a  turbo-compressor  are  shown  drawn  to  scale. 
Arbitrarily,  a  certain  rate  of  delivery  has  been  called  unity, 
and  just  as  arbitrarily  a  certain  speed  has  been  called  unity. 


PRESSURE  GOVERNORS 


157 


Let  PC  be  the  discharge  pressure  which  is  to  be  maintained 
constant,  on  the  assumption  that  intake  pressure  is  naturally 
constant.  (If  both  intake  and  discharge  pressures  are  subject 
to  change,  matters  are  more  complicated.)  The  characteristics 
show  that  2 1  %  of  change  of  speed  changes  the  rate  of  delivery 
from  .81  to  1.06,  or  roughly  26%.  This  behavior  of  turbo- 
compressors  has  been  cited  as  a  great  advantage,  because, 
with  constant  speed  governing,  the  pressure  changes  so  little 
over  quite  a  wide  range  of  delivery.  This  property  is  indeed 
an  advantage  in  cases  where  the  demand  (for  air,  for  instance) 
stays  within  narrow  limits,  because  then  pressure  governing  is 
reduced  to  the  common  and  well-worked-out  problem  of  speed 
governing.  It  may  be  noted  in  passing  that  this  part  of  a  turbo- 
compressor  characteristic  differs  radically  from  the  displace- 
ment pump  characteristic  (Fig.  106).  In  one  case  the  curve  is 
almost  horizontal ;  in  the  other  case  it  is  almost  vertical.  Re- 
turning to  the  case  in  question,  it  must  be  stated  that  cases  of 
limited  range  of  delivery  almost  invariably  turn  into  cases  of 
wide  range  of  delivery  in  the  course  of  time,  so  that  the  ad- 
vantage is  more  apparent 
than  real.  The  relation 
between  speed  variation 
and  delivery  variation 
for  a  given  constant  dis- 
charge pressure  is  ap- 
parent from  the  nest  of 
characteristics.  If  the 
demand  drops  below  a 
certain  critical  value  V, 
which  equals  about  .75 

in  the  diagram  Fig.  107,  the  pressure  can  no  longer  be  kept 
constant,  but  drops  rapidly  to  p0,  rises  again  to  pc  under  the 
influence  of  the  governor,  drops  back  to  p0,  and  so  forth.  The 
turbo-machine  surges  or  pumps,  unless  special  governing  devices 
are  provided  which  either  throttle x  the  inlet,  or  bleed  the 
discharge. 

From  a  comparison  of  displacement  and  velocity  charac- 
teristics it  is  evident  that  maintaining  constant  pressure  against 


E 

U 

5 

S- 



—  —  — 

=£1 

-  ~. 

•^i.^,^^ 

V 

C  ET 







^^ 

s     S 

N 

—  O. 

ajnssa 

F 

c 

sl 

5 

,. 

X 

15 

a 

Volume  or  weight  taken  in 
In  unit  time.  — 


FIG.  107 


158    GOVERNORS  AND  THE   GOVERNING  OF  PRIME  MOVERS 

a  variable  demand  requires  much  greater  change  of  speed  in 
displacement  machinery  than  it  does  in  turbo-machinery. 

Turning  now  to  the  regulating  devices  used  for  maintaining 
constant  pressure  against  a  variable  demand,  we  see  immediately 
that  we  have  two  possibilities  for  regulation,  namely  (1)  to 
keep  the  speed  of  the  pump  and  prime  mover  constant  and  to 
vary  the  output  of  the  pump  proper,  and  (2)  to  vary  the  speed 
of  the  prime  mover.  Method  No.  1  is  obviously  independent 
of  the  type  of  prime  mover,  and  may  be  applied  just  as  well  if 
the  pump  is  driven  by  an  electric  motor  or  by  belt  from  a  line 
shaft.  Devices  for  varying  the  output  of  the  pump  in  spite  of 
constant  angular  velocity  were  indeed  originally  developed  for 
belt-driven  and  for  motor-driven  pumps.  Although  they  are 
now,  for  the  sake  of  uniformity  of  pump  design,  frequently 
used  on  engine-  or  turbine-driven  pumps,  they  do  not  belong 
in  a  book  on  the  governing  of  prime  movers,  and  will  not  be 
described  here.1  In  the  application  of  the  second  method  the 
most  natural  step  to  be  taken  consists  in  deriving  a  force  from 
the  pressure  produced  by  the  pump  and  in  opposing  it  by  a 
known  force,  as  indicated  in  paragraph  1  of  Chapter  I.  Any 
difference  between  the  two  forces  is  used  to  move  the  energy- 
controlling  mechanism.  This  method  leads  to  devices  which 
are  diagrammatically  illustrated  in  Figs.  108,  109  and  110. 
In  these  illustrations  no  attempt  has  been  made  to  impart 
features  of  machine  design.  In  these  devices  the  pressure, 
acting  upon  some  form  of  piston,  tends  to  lift  a  weight  (1)  or 
to  deform  a  spring  (2),  or  to  do  both.  If  the  weights  (1)  only 
are  used,  the  tendency  is  to  maintain  a  constant  pressure  irre- 
spective of  the  position  of  the  float,  bellows,  or  piston.  If  the 
force  of  a  spring  such  as  indicated  by  (#),  Fig.  108,  is  added  to 
the  weight,  the  tendency  is  to  adjust  a  different  pressure  for 
each  position  of  the  float,  bellows,  or  piston. 

In  this  description,  the  phrase  "the  tendency  is  to"  was 
used  advisedly,  because  these  devices  will,  under  certain  con- 
ditions, govern  satisfactorily,  and  will  result  in  abominably 

1  The  principal  means  used  are  by-passes,  throttling  of  inlet,  keeping  inlet  or 
outlet  valves  open,  varying  clearance  space,  starting  and  stopping;  many  of  them 
are  known  as  unloading  devices. 


PRESSURE   GOVERNORS 


159 


poor  regulation  under  different  conditions.  The  safest  way  to 
determine  which  of  the  two  will  happen  would  be  to  derive  and 
discuss  the  complete  differential  equations  of  motion.  But 
pressure  regulation,  as  before  stated,  has  one  more  variable 
than  speed  regulation,  which  makes  the  differential  equations 
of  pressure  regulation  more  complicated  than  those  of  speed 
regulation.  For  that  reason  an  attempt  will  be  made  to  con- 
struct a  limiting  case  between  stability  and  instability  in  a 
manner  similar  to  that  followed  in  speed  governing.  This 


FIG.  108 


FIG.  109 


limiting  case  will  be  derived  with  the  aid  of  Fig.  Ill,  which 
represents  a  diagram  of  an  air  or  gas  pump  (2)  delivering 
into  a  container  of  volume  F2  from  which  the  fluid  is  discharged 
in  a  steady  stream  through  a  nozzle  (1).  Let  the  pump  deliver 
Vfu  cubic  feet  of  fluid  per  second,  where  u  is  the  average  angular 
velocity  of  the  pump.  Valve  (4)  controls  the  flow  of  steam  to 
the  prime  mover  (not  shown)  operating  the  pump.  Now  let 
the  governor  be  set  in  motion  up  and  down.  Under  what  con- 
ditions will  governor,  speed  and  pressure  perform  sine  harmonic 
vibrations  about  the  values  of  equilibrium? 


160     GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


Let  x  be  the  displacement  of  the  governor  from  equilibrium 
position,  then 

du=_^M^ 

dt  Ao    I 

which  is  true  upon  the  assumption  that  x  is  small,  which  means 
that  the  pressure  variations  are  so  small  as  not  appreciably 
to  affect  the  unbalanced  moment.  A0,  as  before,  is  the  whole 

governor  travel,   Mm  is  the   maximum 

torque,  and  I  is  the  moment  of  inertia  of 

all  rotating  parts. 

Let  Du  be  the  angular  velocity  in 

excess  of  the  average  ;  then  we  find  the 


*  Position 
of  Equilibrium 


FIG.  110 


FIG.  Ill 


pressure  rise  in  time  dt  from  (DuV'dt  +  V2)p  =  Vz(p  +  dp)  from 
which  we  have 

V 
dp  =  Du  —  pdt (2) 

V  2 

Turning  to  Fig.  112,  assume  that  the  governor  performs 
sine  harmonic  vibrations  of  the  amplitude  \A.  Then  the  speed 
will  also  fluctuate  up  and  down  with  a  phase  lag  of  90°  behind 
the  governor  motion.  But  with  a  container  as  shown  in  Fig. 


PRESSURE    GOVERNORS 


161 


111,  the  pressure  lags  90°  behind  the  speed,  the  pressure  being 
a  maximum  when  the  excess  speed  disappears.  This  means 
that  the  pressure  lags  180°  behind  the  governor.  Hence,  the 
pressure  change  is  (negatively)  proportional  to  the  governor 
displacement,  and  the  pressure  curve  in  Fig.  112  is  a  straight 
line  (1)(4)>  Comparing  Fig.  112  with  Fig.  Ill,  we  note  that 
excess  pressure,  such  as  that  at  point  (4),  urges  the  governor 
still  farther  away  from  mid-position.  But  to  get  sine  harmonic 
motion,  we  must  subject  the  governor  to  a  force  which  pulls 


FIG.  112 


it  back  to  equilibrium  position  and  which  is  proportional  to 
the  displacement  x.  A  stability  spring  must  therefore  be  added 
to  return  the  governor.  If  line  (2)  (3)  in  Fig.  112  represents 
(negatively)  the  spring  forces,  then  only  the  difference  between 
spring  force  and  excess  pressure  force  is  available  for  returning 
the  governor,  as  indicated  by  vertical  section-lining. 

The  angular  velocity  w  of  the  auxiliary  vector  of  the  sine 
harmonic  vibration  is  determined  by  the  section-lined  ordinates, 


because  w  =  \J ,  where  PI  is  the  restoring   force   at   unit 


m 


displacement.     At  the  end  of  the  governor  swing  the  restor- 


162    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

^ 
ing  force  is  (3)  (4)  =  (3)  (6)  -  (4)  (6)  or  —Si  -  G  D0p,  where  Si 

is  the  spring  force  for  unit  deformation,  G  =  cross-sectional 
area  of  governor  float,  D0p  =  excess  pressure  at  the  end  of 
governor  swing.  Now  suppose  the  stiffness  Si  of  the  spring 
to  be  adjustable.  Make  the  spring  more  flexible.  Then  w  will 
become  smaller,  the  excess  speed  will  grow,  and  the  excess 
pressure  will  grow.  The  section-lined  strip  becomes  smaller, 
first,  because  point  (3)  comes  down,  and  second,  because 
point  (4)  goes  up.  A  limit  is  soon  reached.  There  must  be 
a  minimum  scale  Si  min  to  the  spring  to  make  return  of  the 
governor  possible.  If,  on  the  other  hand,  the  spring  is  made 
stiffer,  the  motion  of  the  governor  is  quickened,  and  both  excess 
speed  and  excess  pressure  tend  to  become  smaller.  It  should, 
however,  be  understood  that  during  the  process  of  changing 
from  the  steady  vibration  with  large  amplitude  to  another 
steady  vibration  with  smaller  amplitude,  the  three  deviations 
of  governor  displacement,  speed  and  pressure  will  fall  out  of 
step  for  a  while  and  will  cause  quite  heavy  fluctuations. 

The  minimum  spring  scale  necessary  for  stability  is  easily 
computed.  For  sine  harmonic  vibration  with  angular  velocity 
w  of  auxiliary  vector,  equation  (1)  becomes 

du      1  A  .  Mm 


1  A  M 

From  which  Du  =  -  —  sin  (wf) 


> 
2  A  0  Iw 


Substitute  this  in  equation  (2)  then 
V      1  A  Mm 


p  here  represents  the  average  value  of  the  pressure  in  F2.    By 

inf.fkcrrot.irm    \\rn    rVKfain 


integration  we  obtain 

V      1  A  M 


PRESSURE    GOVERNORS  163 

with  a  maximum  value  at  end  of  swing  of 

1  A  V'p  Mm 
°P  "  2A0  V*  I  w2' 


flSi      D0p  G 

But  we  also  have        w  =  \l  —  —  -  —  • 

m       A       m 

2~ 

The  two  expressions  for  w  must  be  equal,  hence 

Si        Pop    G  _  1  A  V'p  Mm    1 
m  \A  m      2A0  V*    I    D0p 

This  equation  may  be  solved  for  Si  or  for  D0p.     It  is  more 

jj    /Y\    A     /yy) 

instructive  to  do  the  latter.    By  multiplication  with  -  ^-—^  —  > 

Z(JT 

we  get  an  equation  of  the  form  (D0p)2  —  K\.D0p  =  —  K2) 
from  which  D0p=  %Ki  ±  V  (%Ki)2  -  K2,  or,  by  substitution 
of  the  values  of  the  constants, 


_  1  S,A         /lSiAy     I  A  V'p  M,,  Am 

"4"e"   ^Vi^V'aZITT  /  20' 

From  this  equation  it  follows  that  there  may  be  a  great  or 
a  small  pressure  rise  for  a  given  spring  force,  as  long  as  the 
value  of  the  radical  is  real.  If  the  latter  becomes  zero,  then 
we  work  with  the  minimum  spring  scale.  Hence  we  have 

1  A  V'p  Mm  A    m 


16    G2        2A0  72    I    2     G 


By  the  introduction  of  time  elements,  this  equation  may  be 
simplified.     We  know  that  —  ~  =  —  ,  also  that  -     -  =          .  > 

L  JL    8  fYlA.  0  \J.g) 


164    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

where  T  g  is  governor  traversing  time  under  the  influence  of 
pressure ;  V'uTf  =  F2,  where  Tf  is  the.  time  required  to  fill  the 
volume  of  the  container.  Then  we  obtain 


(5) 


for  the  smallest  permissible  scale  of  the  spring. 

From  this  equation  the  static  pressure  fluctuation  can  be 
found,  because 

pressure   difference    (Between   extreme   positions)  X  governor   area 
=  spring  scale  X  governor  travel,  hence  when 

static  pressure  difference  between  extreme  positions 
p  =  —  —  > 

average  pressure 


The  conclusion  from  this  reasoning  is  that,  for  stability  of 
regulation,  the  governor  must  have  a  minimum  static  pressure 
fluctuation,  just  as  in  speed  governing  the  governor  had  to 
be  designed  for  a  minimum  static  speed  fluctuation.  For  many 
classes  of  service  such  a  fluctuation  is  admissible,  but  occa- 
sionally very  close  pressure  regulation  is  desired  ;  a  static 
fluctuation  is  not  permissible  in  such  a  case,  and  temporary 
stability  must  be  secured  by  other  means.  Among  such  means 
are  compensating  dashpots,  similar  to  those  used  in  speed 
governing  (Chorlton-Whitehead  governor,  Bee  governor,  etc., 
see  paragraph  2,  Chapter  IX),  or  throttling  of  the  inlet  to  the 
governor  such  as  at  point  (3),  Fig.  Ill,  or  inclosure  of  the 
governor  in  an  almost  airtight  box. 

The  question  of  stability  of  regulation  being  settled,  the 
problem  arises,  what  must  be  done  to  damp  the  vibrations  out 
of  existence?  The  device  used  in  speed  governing,  namely 
damping  by  an  oil  gag  pot,  does  not  work  in  this  case,  as  will 
readily  be  understood  from  Fig.  112.  The  period  of  a  damped 
vibration  is  longer  than  that  of  an  undamped  vibration,  hence 
the  speed  rise  is  greater,  and  the  excess  pressure  becomes 


PRESSURE    GOVERNORS 


165 


greater  (instead  of  smaller,  as  desired)  ;  the  governor  does  not 
return  promptly.  Another  method  of  arriving  at  the  same 
conclusion  consists  in  arresting  the  governor  at  point  (5), 
Fig.  112,  until  the  speed  has  dropped  to  normal.  During  that 
time  the  pressure  rises  considerably.  As  soon  as  the  governor 
is  released  there  is  no  force  to  return  it,  and  it  crawls  farther 
away  from  the  equilibrium  position  under  the  influence  of 
accumulated  pressure. 

While  governor  displacement  damping  fails,  "  speed  damp- 
ing" does  the  trick.  If  in  Fig.  113,  which  is  a  reproduction  of 
part  of  Fig.  112,  the  speed  should  not  rise  quite  as  high  on  the 
travel  to  the  right,  and  should  not  fall  quite  as  low  on  the 
travel  to  the  left,  then  the  pressure  fluctuation  would  be  re- 
duced, more  restoring  force  would  be  effective,  the  governor 
would  quicken  in  its  movements,  the 
pressure  fluctuation  would  become  still 
less,  etc.,  and  the  vibration  would 
cease.  This  desirable  effect  is  produced 
by  throttling  both  in  the  ports  and 
valves  of  the  prime  mover,  and  in  those 
of  the  pump.  For  a  given  position  of 
the  power-controlling  mechanism, 
throttling  makes  more  of  the  engine  or 
turbine  torque  available  at  low  speed, 
and  reduces  it  at  high  speed.  The 
speed  is  reduced  during  the  excess  speed  period,  and  is  increased 
during  the  speed  deficiency  period  ;  it  will  follow  a  line  some- 
what like  the  dotted  spiral  of  Fig.  113,  and  the  vibrations  will 
rapidly  die  out. 

Summing  up,  the  devices  shown  in  Figs.  108,  109  and  110 
may  work  satisfactorily,  and  may  not.  Satisfactory  regula- 
tion is  favored  by  long  starting  time  Ts  (large  flywheels), 
long  filling  time  Tf  (large  container),  and  small  governor 
traversing  time.  Stability  of  regulation  requires  static  pressure 
fluctuation  or,  where  such  fluctuation  is  not  permissible,  tem- 
porary stability.  Throttling  in  valves  and  ports  of  prime 
mover  and  pump  damps  vibrations  out  of  existence. 

Pure  pressure  governing  of  the   character  here   described 


FIG.  113 


166    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


occurs  seldom.  As  a  rule,  the  container  is  a  piping  system  of 
small  cross-sectional  area  compared  to  its  length,  see  dotted 
lines  in  Fig.  111.  In  that  case  any  increase  of  speed  immedi- 
ately causes  an  increase  of  pressure  at  the  mouth  of  the  pump, 
on  account  of  the  friction  in  the  pipe.  The  pressure  does 
not  lag  90°  behind  the  speed.  It  has  a  component  which  is  in 
phase  with  the  speed  and  a  component  which  is  90°  behind  the 
speed.  In  a  vibration  diagram  with  abscissae  representing 
governor  displacement,  the  component  in  phase  with  the 
speed  is  represented  by  an  ellipse  with  the  governor  displace- 
ment as  an  axis,  while  the  component  lagging  90°  behind  the 
speed  is  represented  by  an  inclined  straight  line,  as  before. 
The  resultant  phase  depends  upon  the  relative  magnitude  of 

the  two  components  (see  Fig.  114,  where 
the  inclined  ellipse  resulting  from  a  com- 
bination of  the  two  phases  has  been 
shown.)  We  then  face  the  peculiar  situa- 
tion that  the  speed  component  requires 
speed  regulation,  and  the  pressure  com- 
ponent requires  pure  pressure  regulation. 
For  the  sake  of  the  speed  component 
FIG.  114  an  adjustable  oil  gag  pot  is  usually 

necessary,  unless  displacement  damping  can  be  secured  by  other 
means. 

Friction  in  pressure  governors  is  just  as  harmful  as  friction 
in  speed  governors,  if  close  regulation  is  desired.  It  produces 
a  " detention  by  friction"  and  endless  fluctuations  of  pressure, 
unless  it  is  eliminated.  Just  as  before,  impressed  cyclical 
vibrations  of  pressure  (caused,  for  instance,  by  the  pulsating 
delivery  of  displacement  machines),  jarring  and  vibration 
transmitted  mechanically  to  the  governor,  and  impressed 
cyclical  forces  eliminate  friction.  In  the  absence  of  these 
agents,  a  frictionless  governor  must  be  used ;  this  means 
knife  edges,  roller  or  ball  bearings,  and  floats  or  bellows  (Figs. 
108  and  109)  in  preference  to  pistons  (Fig.  110).  If  the  latter 
design  must  be  used  on  account  of  high  pressure,  good  lubrica- 
tion and  plenty  of  oil  grooves  for  distributing  the  pressure  uni- 
formly around  the  piston  are  a  great  help  ;  because  absence 


PRESSURE   GOVERNORS  167 

of  such  grooves,  coupled  with  local  deformation  due  to 
high  pressure,  forces  the  plunger  to  one  side  and  causes  it  to 
stick. 

All  prime  movers  regulating  for  constant  pressure  must 
also  be  equipped  with  a  speed  limit  centrifugal  governor  so 
that  excessive  demands  upon  pump  or  compressor  will  not 
wreck  the  outfit.  Such  runaway  governors  may  be  (and  usually 
are)  of  very  simple  design,  because  they  enter  into  action  only 
occasionally,  and  because  all  pretense  to  close  regulation  is 
abandoned  when  they  do  enter  into  action.  Of  course  they 
must  be  strong  enough  to  handle  the  valve  gearing. 

While  pressure  governing  by  the  devices  shown  in  Figs. 
108,  109,  and  110  is  successful  with  proper  design  when  a  single 
prime  mover  and  pump  work  against  the  demand  for  air, 
water,  or  gas,  the  assistance  of  a  centrifugal  governor  cannot 
be  spared  as  soon  as  two  or  more  units  work  in  parallel  (deliver 
to  the  same  container).  For  proof  of  this  statement  study 
the  action  of  two  steam-driven  compressors  jointly  furnishing 
compressed  air  to  a  mine.  Let  these  compressors  be  of  a  high 
class  type,  with  steam  cut-off  governed  by  pressure  governors, 
such  as  shown  in  Fig.  110.  Let  one  governor  have  a  little 
more  friction  than  the  other.  Now  let  the  steam  pressure  drop 
gradually.  Then  the  governor  with  less  friction  will  adjust 
its  engine  and  will  maintain  the  pressure.  The  governor  with 
more  friction  will  not  move,  because  the  pressure  is  main- 
tained constant  by  the  other  governor ;  its  engine  will  not 
receive  enough  steam,  and  the  compressor  will  slow  down 
considerably,  causing  the  other  machine  to  speed  up  an  equal 
amount.  As  a  makeshift,  one  of  the  machines  is  sometimes 
operated  at  constant  speed  by  a  centrifugal  governor,  all  the 
regulating  being  done  by  the  second  machine.  This  will  do 
in  the  case  of  two  machines,  but  when  three  or  more  run  in 
parallel,  the  fluctuations  are  too  severe  to  be  taken  care  of  by 
one  pressure  governor  and  compressor  only. 

In  order  to  make  all  machines  share  evenly  (or  nearly  so)  in 
the  delivery,  a  combination  centrifugal  and  pressure  governor 
is  frequently  used.  The  principle  of  such  a  combination  gov- 
ernor is  shown  in  Fig.  115.  A  centrifugal  governor  (1)  of  great 


168    GOVERNORS  AND  THE  GOVERNING   OF   PRIME   MOVERS 

static  fluctuation,  such  as  described  in  Chapter  V,  controls 
one  end  of  a  floating  lever  (2).  The  other  end  of  the  latter  is 
controlled  by  a  pressure  governor  (4)  of  the  type  shown  in 
Fig.  110.  Point  (3)  of  the  floating  lever  controls  the  supply 
of  energy  to  the  prime  mover.  Variable  demand  for  air  (or 
other  fluid  pumped)  at  practically  constant  pressure  means 
speed  of  prime  mover  fluctuating  with  the  demand.  Point  (3) 
will,  in  high  class  reciprocating  units,  maintain  practically  tho 
same  position  for  any  speed,  except  that  it  will  move  temporarily 
for  the  purpose  of  accelerating  or  retarding  the  pump.  The 
result  is  that,  as  a  first  approximation,  the  floating  lever  always 

passes  through  the  same  point 
(5),  while  the  two  ends  move. 
It  is  to  obtain  great  speed  varia- 
tion over  this  range  of  move- 
ment that  the  centrifugal  gover- 
nor is  arranged  with  excessive 
speed  fluctuation.  In  principle 
this  governor  is  identical  with 
the  governor  described  in  Chap- 
ter V.  Naturally  a  safety  device 
must  be  used  to  prevent  over- 
speeding  in  case  of  the  pressure 
main  or  the  pipe  to  the  pressure 
governor  breaking.  Any  of  the 
devices  mentioned  in  Chapter  V 
may  be  used.  For  the  sake  of 
completeness  an  additional  and 
different  arrangement  is  illustrated  in  Fig.  115.  The  necessary, 
great  static  fluctuation  is  obtained  by  a  combination  of  static 
properties  of  the  governor  proper  (1)  and  of  a  central  spring  (7)  ; 
the  maximum  tension  of  the  latter  is  determined  by  a  weight  (5) , 
which  normally  rests  on  a  fixed  stop  (6)  and  which,  in  the  just 
mentioned  case  of  overspeeding,  is  carried  by  the  spring  (7) 
acting  upon  a  lever  with  fulcrum  (8). 

The  combined  speed  and  pressure  governor  distributes  the 
work  evenly,  provided  that  the  pressure  governor  is  set  with 
a  sufficient  static  pressure  fluctuation.  To  see  that  the  governor 


Less?  "Steam 
More  Steam 


FIG.  115 


PRESSURE    GOVERNORS  169 

fills  the  bill,  imagine  that  one  compressor  has  lagged  behind 
the  others ;  the  speed  governor  end  of  lever  (2)  will  drop  and 
point  (3)  will  move  down  and  give  more  steam,  unless  point  (4) 
on  the  pressure  side  goes  up.  But  the  latter  cannot  occur, 
because  it  would  unbalance  the  pressure  governor.  Hence 
more  steam  is  given,  and  the  slow  machine  is  speeded  up. 

References  to  Bibliography  at  end  of  book:  54,  75,  81. 


CHAPTER  XIII 

RELAY  GOVERNING 

1.  Reasons  for  the  Use  of  Relay  Governors  and  Forces  Acting 
upon  Them.  —  In  the  preceding  chapters  the  governor  was 
studied  in  its  two  capacities  of  measuring  instrument  and  of 
motor  for  adjusting  the  valve  gear.  In  the  present  chapter,  we 
will  investigate  the  properties  of  governors  the  motive  power 
of  which  need  only  be  large  enough  to  release  and  control 
another  source  of  energy  which,  in  turn,  adjusts  the  power- 
controlling  mechanism  of  the  prime  mover. 

The  use  of  relay  governors,  as  this  type  is  called,  dates 
back  to  about  1870,  but  their  development  remained  slow  until 
the  electric  generator  demanded  precise  regulation  of  large 
hydraulic  turbines.  In  that  type  of  prime  mover,  frictional 
resistance  to  motion  of  power-controlling  mechanism  is  espe- 
cially great,  so  that  direct-control  governors  were  out  of  the 
question.  In  the  development  of  this  type  of  governor,  American 
engineers  played  a  leading  part.  Relay  governing  for  hydraulic 
turbines  was  so  successful  that  the  same  method  of  governing 
was  transferred  to  steam  turbines  and  to  large  gas  engines. 
While  in  steam  turbines  the  resistance  to  adjustment  of  steam- 
controlling  mechanisms  can  be  kept  comparatively  small,  the 
dynamic  action  of  steam  flow  causes  widely  varying  forces 
upon  the  governor  in  different  parts  of  its  travel  (compare 
paragraph  3  of  Chapter  III),  unless  the  controlling  mechanism 
is  designed  with  great  care  and  knowledge.  In  the  latter  case 
direct-control  governors  are  quite  feasible  and  are  indeed  used 
with  steam  turbines  passing  up  to  30,000  pounds  of  steam  per 
hour.  In  larger  machines  direct-control  governors,  even  with 
careful  design,  become  so  large  and  expensive  that  it  pays  to 
use  relay  governors  instead.  Frequently,  relay  governors  are 
adopted  for  smaller  sizes  also  in  order  to  obtain  uniformity  of 
design. 

170 


RELAY   GOVERNING  171 

Many  large  gas  engines  are  equipped  with  relay  governors, 
because  the  resistance  of  the  gas-controlling  valves  is  uncertain 
on  account  of  dust  and  tar  in  the  gas.  Tarry  matter  in  the  gas 
will  easily  increase  the  resistance  of  the  valves  to  50  (or  more) 
times  the  value  of  the  resistance  of  the  valves  with  clean  gas. 

Last,  not  least,  a  relay  frees  the  governor  (measuring  instru- 
ment) from  the  troublesome  integrated  effect  of  valve-gear 
reactions,  which  effect  is  so  difficult  to  predetermine  correctly. 

The  very  nature  of  relay  governing  involves  certain  differ- 
ences between  it  and  direct-control  governing,  and  these  dif- 
ferences should  be  clearly  understood.  The  purpose  of  relay 
governing  is  to  keep  all  valve  gear  forces  away  from  the  gov- 
ernor. In  consequence,  the  friction-eliminating  influence  of 
vibratory  impressed  forces  is  absent.  In  relay  governors  there 
are  no  cyclical  vibrations  due  to  vibratory  reactions,  and 
detention  by  friction  (see  paragraph  4  of  Chapter  II)  becomes 
of  great  importance.  The  absence  of  vibration  forces  has  be- 
come more  complete  with  the  perfection  in  the  production  and 
lubrication  of  toothed  gears  used  for  driving  the  governors. 
The  old-time  jarring  of  the  governor  due  to  rough  gears  is  not 
found  in  steam  turbines.  And  finally,  turbines  have  no  cyclical 
variation  of  angular  velocity  such  as  steam  and  gas  engines 
have  ;  this  does  away  with  another  friction-reducing  agent. 

These  three  facts  have  necessarily  resulted  in  the  use  of 
relay  governors  with  smallest  possible  internal  friction.  Knife- 
edge  joints  have  become  universal  in  the  type  of  governors 
under  discussion.  Even  small  friction  in  centrifugal  governors 
of  this  type  produces  never-ending  vibrations.  The  latter  are 
especially  noticeable  when  the  load  is  constant. 

Mr.  C.  A.  Parsons,  one  of  the  foremost  pioneers  in  steam 
turbine  design,  recognized  this  situation  at  a  very  early  date, 
and  overcame  governor  friction  by  means  of  impressing  a 
vibration  upon  the  governor.  This  was  accomplished  by  an 
eccentric  in  connection  with  an  oil  gag  pot.  His  system  of 
governing  became  known  as  "puff  governing/'  because  steam 
was  admitted  in  puffs.  Several  turbine  builders  make  use  of 
this  principle  at  the  present  time ;  they  have,  however, 
reduced  the  governor  vibration  to  a  very  small  amount,  just 
sufficient  to  eliminate  friction. 


172     GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

A  second  difference,  and  an  important  one,  results  from  the 
addition  of  a  variable.  The  governor  releases  a  force,  which 
action  takes  time.  Then  the  force  adjusts  the  energy-controlling 
mechanism,  which,  again,  takes  time.  Now  it  may  be  that 
the  sum  of  these  two  time  elements  is  less  than  the  time  which 
a  direct-control  governor  would  require  for  the  same  work, 
but  a  new  variable  has  been  added  nevertheless.  Instead  of 
dealing  only  with  the  promptness  or  traversing  time  of  the 
governor,  we  now  deal  with  the  latter  plus  the  promptness  or 
traversing  time  of  the  relay.  In  future  calculations  this  time 
will  be  used.  It  is  denned  as  that  time  which  is  required  by 
the  relay  mechanism  (hydraulic  cylinder,  electric  motor,  gear- 
ing from  prime  mover)  to  move  the  power-controlling  mechanism 
(valve  gear,  throttle  valve,  hydraulic  gate)  from  full-load 
position  to  no-load  position.  The  symbol  Tr  will  be  used  for 
the  relay  traversing  time,  while  T a  will  be  retained  for  governor 
traversing  time. 

What  has  just  been  stated  with  regard  to  introducing  an 
additional  time  element  applies  with  equal  force  to  additional 
detention  by  friction.  The  regulating  or  relay  mechanism 
may  have  considerable  friction  which,  in  some  forms  of  relay 
governors,  is  just  as  harmful  as,  or  even  more  harmful  than 
friction  in  the  governor  proper. 

A  third,  and  extremely  vital,  difference  between  direct- 
control  governing  and  relay  governing  is  that  the  latter  enables 
the  designer  practically  to  get  rid  of  the  troublesome  influence 
of  mass  of  governor.  This  is  accomplished  by  methods  which 
use  only  a  very  short  governor  travel  and  which  will  be  described 
in  detail  later  on. 

A  fourth  difference  lies  in  the  fact  that  relay  governors 
are  easily  adapted  to  obtaining  reversed  speed  curves.  This 
latter  property  of  relay  governors  was  brought  out  in  the 
governing  of  hydraulic  turbines  with  long  supply  lines.  In 
such  governors,  gate  movements  must  be  slow  (unless  stand- 
pipes  or  surge  tanks  are  provided),  to  protect  the  line  from 
water  hammer.  This  requirement  necessitates  a  governor  of 
great  static  fluctuation  for  the  sake  of  stability  of  regulation. 
But  great  static  fluctuation  means  a  great  speed  difference 


RELAY  GOVERNING  173 

between  no  load  and  full  load,  which  is  not  permissible  in  elec- 
tric lighting.  This  predicament  led  to  the  invention  of  auto- 
matic speed-restoring  devices  which  gradually  bring  the  speed 
back  to  normal  after  every  change  of  load.  These  devices  will 
be  found  described  later  on. 

The  sources  of  energy  which  are  released  by  the  governor 
are  either  fluid  pressure,  or  else  electrical  energy,  or  finally 
mechanical  energy  derived  from  the  prime  mover.  Fluid  pres- 
sure may  be  derived  from  steam,  oil,  or  water  under  pressure, 
or  from  compressed  air.  Steam  and  compressed  air  are  elastic, 
or  expansive,  so  that  relay  pistons  operated  by  these  fluids 
tend  to  cause  overtravel  and,  in  consequence  of  that,  racing 
and  hunting.  Frictional  damping  will  stop  this,  but  introduces 
speed  fluctuations  from  another  source.  Water  and  oil  are 
superior  in  this  respect.  Water  often  carries  impurities  which 
wear  out  the  pilot  valve.  Oil  under  pressure  is  doubtless  the 
best  fluid  for  hydraulic  relay  governors. 

Electrical  energy  has  occasionally  been  used  for  relay  gov- 
erning of  prime  movers,  but  has  been  given  up  on  account  of  the 
greater  convenience  of  steam  and  pressure  oil.  It  is  used  to  a 
much  greater  extent  for  regulation  purposes  outside  of  power 
plants  where  the  transmission  of  steam  and  pressure  oil  is  incon- 
venient and  for  regulating  prime  movers  which  keep  constant 
some  quantity  at  a  considerable  distance  from  the  power  house. 

The  use  of  the  mechanical  energy  of  the  prime  mover  is 
very  inviting  at  first  thought,  but  in  practice  many  difficulties 
must  be  overcome.  Heavy  clutches  must  be  thrown  in,  held 
in  place,  and  pulled  out.  Wear  occurs  in  these  clutches,  and 
must  be  taken  care  of  automatically.  So  difficult  is  a  satisfac- 
tory solution  that  in  modern  mechanical  relay  governors  the 
clutch  is  operated  by  a  hydraulic  cylinder,  which  latter  is  con- 
trolled by  a  relay  valve.  Such  a  governor  may  be  called  a 
combination  hydraulic  and  mechanical  relay  governor. 

References  to  Bibliography  at  end  of  book:  8,  9,  10,  12,  14,  16,  19,  20,  21,  24, 
27,  29,  36,  38,  41,  44,  45,  46,  47,  48,  53,  55,  56,  60,  66,  67,  69,  71,  73,  75,  76,  77, 
78,  81,  82,  83. 

2.  Relay  Mechanisms.  —  While  relay  mechanisms  necessar- 
ily vary  with  the  forces  which  are  brought  into  action  by  the 


174    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


governor  (measuring  instrument),  there  are  certain  principles 
which  must  be  observed  in  any  type  of  relay  governor ;  and 
since  the  hydraulic  governor  is  the  one  most  commonly  used, 
the  principles  in  question  will  be  demonstrated  with  reference 
to  that  type  of  governor.  Application  of  the  same  principles 
to  mechanical  or  electrical  relays  will  not  be  difficult. 

In  the  following  illustrations  the  governor  (measuring 
instrument)  is  represented  by  the  symbol  G'r.  The  type  shown 
is  a  centrifugal  governor  which  measures  angular  velocity.  But 
the  operation  of  the  different  mechanisms  would  remain  exactly 
the  same  if  the  centrifugal  governor  were  replaced  by  a  constant- 
volume  governor  as  shown  in  Chapter  XI,  or  by  a  constant- 
pressure  governor  as  shown  in  Chapter  XII. 

Figure  116  illustrates  a  very  simple  arrangement,  which, 
unfortunately,  is  even  now  used  by  those  who  have  not  taken 

time  to  study  governors.  The 
arrangement  is  faulty,  as  will 
appear  from  the  following 
reasoning  :  Consider  a  governor 
and  prime  mover  in  which  the 
governor  and  the  relay  have  the 
right  position  for  equilibrium ; 
then  imagine  the  governor  sud- 
denly depressed  from  equilibrium 
position,  point  (2),  Fig.  117,  to 
point  (1),  and  then  released. 
Under  the  influence  of  its  own 
stability  (due  to  static  fluctua- 
tion) and  of  an  increase  of  speed,  see  curve  (9)  (12,)  it  will  return 
toward  mid-position  (3).  While  it  does  so,  the  power  piston  has 
traveled  downward,  from  point  (6)  to  point  (8) .  It  reaches  its 
greatest  displacement  when  the  governor  passes  through  mid- 
position  at  point  (3).  During  all  this  time  the  speed  grows.  The 
rate  of  increase  of  speed  is  greatest  at  point  (12).  Beyond  the 
line  (3)  (8)  (12)  the  governor  travels  upward  under  the  influence 
of  the  continually  growing  speed.  The  latter  reaches  a  maxi- 
mum in  point  (10)  t  when  the  power  piston  has  returned  to 
mid-position,  point  (7).  The  governor  is  still  driven  upward 


FIG.  116 


RELAY  GOVERNING 


175 


by  a  regulating  force  due  to  the  excess  speed.  The  latter  does 
not  come  back  to  normal  at  point  (11)  until  the  power  piston 
has  traveled  upward  a  considerable  distance.  But  at  that 
time  the  governor  is  not  only  away  a  much  greater  distance  - 
(4)  (^)  —  from  the  position  of  equilibrium  than  it  was  at  the 
beginning  of  the  disturbance — (1)(2) — but  it  also  has 
acquired  considerable  kinetic  energy,  which  carries  it  still 
farther  away  from  correct 
position.  The  amplitude  of 
the  vibration  grows,  until 
the  governor  strikes  a  stop.  .  , 

The  mechanism  is  useless.  Governor  \V 
It  is  true  that  the  arrange-  position  omd\ 
ment  under  discussion  can  P'lot  position 
be  made  to  regulate  after  a 
fashion  by  giving  the  gover- 
nor great  stability  and  much 
damping,  by  making  the 
pilot  valve  very  small  and 
by  using  a  prime  mover  and 
torque  absorber  with  deci- 
dedly self-regulating  proper- 
ties. Even  then  the  device 
will  work  only  on  condition 
that  the  changes  of  load  are  very,  very  gradual.  The  prime 
mover  works  in  that  case  with  long,  slow  vibrations  at  constant 
load  and  with  speed  changes  which  are  severe,  even  if  the  load 
varies  only  a  small  fraction  of  the  total. 


Relay 
position 


Speed  of 
prime  mover 


Time 


FIG.  117 


Rigid  Return  of  Pilot  Valve 

The  shortcomings  of  the  arrangement  shown  in  Fig.  116 
were  recognized  at  an  early  date.  The  movement  of  the  pilot 
valve  was  "  compensated "  for  by  the  addition  of  rod  (5)  with 
fulcrum  (4)  for  lever  (3),  Fig.  118.  The  latter  is  now  a  float- 
ing lever.  If  the  governor  rises,  (4)  is  temporarily  a  fixed  point. 
The  pilot  valve  is  raised,  the  power  piston  moves  down,  turn- 
ing lever  (3)  about  fulcrum  (1)  and  returning  the  freely  movable 


176    GOVERNORS  AND  THE   GOVERNING  OF   PRIME   MOVERS 


pilot  valve  to  mid-  or  closed  position.  The  device  is  known  as 
an  "anti-racing"  device,  or  as  a  " compensating  return/'  or 
simply  as  a  "  return,"  meaning,  of  course,  a  return  of  the  pilot 
valve  to  mid-position.  It  will  presently  be  shown  that  other 
quantities  are  compensated  for  in  relay  governors  so  .that  the 
name  of  "compensator"  for  the  return  should  be  abandoned. 

Since  the  pilot  valve  must  return  to  mid-position  for  power 
equilibrium,  there  belongs  a  definite  position  of  the  governor 
to  each  position  of  the  power  piston  (see  dotted  positions  of 
lever  (5)).  And  since  a  given  angular  velocity  corresponds  to 
each  position  of  the  governor,  it  follows  that  a  definite  angular 
velocity  of  the  governor  (and  of  the  prime  mover)  belongs  to 
each  position  of  the  power  piston.  The  arrangement  is  fully 
equivalent  to  the  direct-control  governor,  except  that  the 
resistance  to  governor  motion  is  minimized  and  that  the  tra- 
versing time  of  the  governor  is  replaced  by  it  plus  relay  tra- 
versing time.  Evidently,  it  is 
desirable  to  make  the  latter  as 
short  as  possible,  but  there  are 
limits,  because  a  short  travers- 
ing time  can  be  obtained  only 
by  means  of  a  large  pilot  valve, 
and  that,  in  turn,  means  greater 
resistance  to  governor  motion. 

The  arrangement  of  Fig.  118 
is  not  the  only  method  of  re- 
turning the  pilot  valve.  The  stem 
(2)  of  the  pilot  valve  may  be 
split  and  may  be  provided  with 
right  and  left  hand  threads  and  a  turnbuckle  for  changing  the 
length.  Many  arrangements  for  returning  pilot  valves  have 
been  made  by  inventors,  and  the  patent  records  are  full  of  return 
mechanisms  in  disguise. 

The  arrangement  which  has  just  been  described  should  be 
called  a  "relay  with  rigid  return"  in  contradistinction  to  those 
with  slowly  yielding  return  which  will  be  described  below. 

The  simple  rigid  return  has  been  almost  universally  adopted 
for  steam  turbine  regulation.  In  order  to  get  along  with  a 


FIG.  118 


RELAY   GOVERNING 


177 


Pilot 
Valve 


very  small  governor  travel,  designers,  as  a  rule,  place  the  pilot 
valve  between  the  governor  and  the  power  cylinder. 

Stabilizing  Relay  with  Limited  Governor  Travel 

Figure  119  illustrates  a  relay  mechanism  which  is  commonly 
ascribed  to  Dr.  Proell  (Zeitschrift  des  Vereines  Deutscher  In- 
genieure,  1884),  and  which  forms  a  bridge  between  the  mechan- 
isms used  for  steam  turbines  and  those  used  in  hydraulic  turbines. 
In  this  mechanism  the  lever  (3)  turns  about  a  fixed  point  (1). 
The  travel  of  the  lever 
is  limited  by  two  lugs 
(4),  and  is  just  sufficient 
to  open  wide  the  ports 
in  the  pilot  valve.  The 
power  piston  is  joined 
to  the  lever  (3)  by  a 
weak  spring  (#),  the 
force  of  which  restores 
the  governor  to  mid- 
position  after  a  disturb- 
ance. When  the  gover- 
nor has  again  reached 
mid-position,  the  power 
piston  has  assumed  a  Fia.  119 

different    position    and 

the  length  of  the  spring  has  been  changed.  By  studying  either 
a  decrease  of  load  or  else  an  increase  of  load  one  sees  readily  that 
for  a  decrease  of  load  the  governor  is  loaded,  which  means  an  in- 
crease of  speed,  and  that  for  an  increase  of  load  the  governor 
is  unloaded,  which  means  a  reduction  in  speed.  The  increase 
or  decrease  is  proportional  to  the  spring  force  and  the  latter, 
in  turn,  is  proportional  to  the  change  of  load.  The  regulating 
mechanism  has,  in  consequence,  a  "static  speed  fluctuation," 
which  is  not,  however,  produced  by  the  properties  of  the 
governor,  but  by  those  of  the  relay  mechanism.  If  the 
travel  of  the  governor  is  made  small  enough,  the  stability  or 
instability  of  the  Jatter  is  of  no  consequence.  While,  with 
this  exception,  the  action  of  this  relay  mechanism  is  just  the 


178    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 


same  as  the  one  of  the  mechanism  shown  in  Fig.  118,  it  should 
be  noted  that  the  travel  of  the  governor  can  be  made  very  small, 
so  that  the  troublesome  effect  of  governor  mass  can  be  prac- 
tically eliminated. 

Relay  Mechanism  with  Slowly  Yielding  Return 

As  before  mentioned,  the  governing  of  hydraulic  turbines 
with  long  penstocks  requires,  on  one  hand,  a  governor  of  great 
static  fluctuation  (in  order  to  save  the  water  lines),  and  on  the 
other  hand  a  governor  of  small  static  fluctuation  in  order  to 
maintain  a  constant  voltage  or  frequency.  For  the  purpose  of 
attaining  both  of  the  apparently  conflicting  requirements,  the 
same  principle  is  used  which  was  described  in  paragraph  2, 

Chapter  IX,  in  con- 
nection with  the 
Chorlton-Whitehead 
governor.  This 
principle,  applied  to 
a  relay  mechanism, 
is  illustrated  in  Fig. 
120.1  It  will  be  re- 
membered that  the 
principle  consists  in 
first  imparting  tem- 
porary stability  to 
the  governor  mecha- 
Va  I  ve  nism,  and  then  gradu- 
ally, by  means  of  an 
oil  pot,  removing  the 

L-L '  stability.   Figure  120 

is  very  similar  to  Fig. 

119.  The  difference  consists  in  the  connection  between  the  power 
piston  and  the  spring  (2).  In  Fig.  119  the  connection  was 
rigid,  whereas  in  Fig.  120  an  oil  gag  pot  (5)  is  interposed. 
If  the  by-pass  on  the  gag  pot  is  closed  (and  if  we  disregard 
the  clearance  between  the  gag  pot  piston  and  its  cylinder), 
the  action  of  the  mechanism  of  Fig.  120  is  identical  with  that 

1  For  the  present,  parts  (6)  and  (7)  should  be  disregarded. 


Power  — 
Cylinder 

No 
load 

^" 

Full 
Loadd 

^ 

L_e__j 

—  . 

tie 

ss 

EH 

1  |  '  ! 

f 

ore 

J 

nr*^1 

\      *- 

} 

RELAY  GOVERNING  179 

of  Fig.  119.  As  a  matter  of  fact,  we  can  best  understand  the 
action  of  the  mechanism  shown  in  Fig.  120  if  we  assume  the 
by-pass  closed  during  a  change  of  load  and  suppose  it  to  be 
opened  after  the  regulating  process  with  rigid  connection  has 
been  completed.  After  the  by-pass  has  been  opened,  spring  (2) 
can  assume  its  free  length,  the  loading  or  stability-producing 
influence  of  the  spring  on  the  governor  disappears,  and  the 
latter  assumes  the  original  speed.  The  action  is  just  the  same 
as  if  the  tension  of  a  loading  spring  in  any  of  the  devices  in 
Chapter  V  were  changed  while  the  governor  is  in  operation. 
Centrifugal  force  and  centripetal  force  are  no  longer  equal, 
and  a  regulating  process  is  started.  In  the  case  in  question  the 
change  of  speed  (or  the  change  of  load)  becomes  more  and  more 
gradual  as  the  spring  tension  disappears. 

The  result  is  a  perfectly  isochronous  governor,  with  stability 
during  the  process  of  regulation.  Oil  pot  (5)  is  commonly 
called  a  "  compensator,"  because  it  compensates  for  the  change 
of  speed  which  would  otherwise  be  caused  by  the  different 
position  of  the  power  piston.  It  might  be  called  a  "  speed 
restorer,"  but  the  term  compensator  is  so  generally  used  that 
it  should  be  retained.  It  should  be  thoroughly  understood 
that  illustration  120  is  purely  diagrammatic.  In  practice  the 
compensator  is  usually  located  some  distance  away  from  the 
power  cylinder  and  is  operated  by  the  latter  through  a  system 
of  levers. 

Slowly-yielding  Return  with  Adjustable  Static  Fluctuation 

Isochronous  regulation,  while  apparently  ideal,  is  not  always 
desirable.  For  parallel  operation  of  synchronous  (alternating 
current)  generators,  a  small,  positive  static  fluctuation  is 
necessary  for  proper  distribution  of  work  among  the  several 
generators  operating  in  parallel.  On  the  other  hand,  asyn- 
chronous generators  require  a  negative  static  fluctuation  (re- 
versed speed  curve).  The  mechanism  of  Fig.  120  can  be  adapted 
to  either  one  of  these  requirements  by  the  addition  of  a  second 
spring  (6)  stretched  between  governor  lever  (3)  and  a  second 
lever  with  fulcrum  (7).  The  bottom  lever  is  attached  to  the 
gag  pot  (not  to  its  piston).  Then  spring  (2),  in  conjunction 


180    GOVERNORS  AND  THE   GOVERNING   OF   PRIME   MOVERS 

with  the  gag  pot,  determines  the  temporary  stability  of  the 
governor,  whereas  the  spring  (6)  determines  the  static  fluc- 
tuation ;  for,  while  spring  (2)  loses  its  tension  after  every  process 
of  regulation,  spring  (6)  does  not.  Observe  that  spring  (6),  in 
the  location  shown  in  Fig.  120,  is  compressed  at  no  load,  and 
is  extended  at  full  load.  This  means  that  the  speed  is  reduced 
at  no  load  and  is  boosted  up  at  full  load.  The  static  fluctuation 
is  negative.  If,  on  the  other  hand,  the  spring  (6)  were  fastened 
to  the  bottom  lever  between  fulcrum  (7)  and  the  gag  pot, 
then  the  static  fluctuation  would  be  positive.  Obviously,  this 
arrangement  lends  itself  to  an  adjustment  of  the  static  fluctua- 
tion while  the  prime  mover  is  in  operation.  To  that  end  the 
auxiliary  spring  must  be  made  movable  right  and  left. 

Adjustment   of   static   fluctuation   may   be   obtained   with 
other  mechanisms,  for  instance  with  the  one  shown  in  Fig.  121, 

which  illustrates  a 
design  with  only  one 
spring,  (1).  The  lat- 
ter is  fastened  to  a 
lever  (4)  with  fulcrum 
(2).  The  extreme  end 
of  the  lever  is  operated 
by  the  gag  pot.  Just 
as  before,  we  split  the 
process  of  regulation, 
assuming  gag  pot  and 
gag  piston  to  be  solid 
during  the  first  part  of 
theprocess.  If  the 
load  drops,  the  gover- 
nor rises,  the  pilot  valve  is  lifted,  the  power  piston  rises, 
returns  the  pilot  valve  and  compresses  the  spring  (1).  Up 
to  this  point  the  mechanism  acts  exactly  like  a  rigid  return, 
such  as  was  shown  in  Fig.  118,  because  the  force  of  the 
deformed  spring  is  taken  up  by  the  power  cylinder  and  has 
nov  action  upon  the  governor  (measuring  instrument).  The 
speed  has  risen  on  account  of  the  static  fluctuation  of  the  cen- 
trifugal governor.  If  now  the  by-pass  in  the  gag  pot  is  opened, 


FIG.  121 


RELAY  GOVERNING  181 

the  spring  (1)  is  free  to  act  slowly  on  point  (5)  of  the  floating 
lever.  The  pilot  valve  is  lifted,  the  power  piston  rises,  returns 
the  pilot  valve,  and  reduces  the  supply  of  energy ;  the  speed 
drops,  the  governor  drops,  raising  the  pilot  valve  ;  the  power 
piston  drops,  bringing  the  supply  of  energy  back  to  the  right 
amount.  If  point  (3)  were  fixed,  the  spring  would  be  free  from 
stress  when  point  (5)  had  returned  to  the  initial  position.  But, 
since  point  (3)  has  been  moved  up  a  small  distance  on  account 
of  lever  (4)  being  linked  to  the  gag  pot,  point  (5)  will  not  quite 
return  to  its  original  position  ;  it  will  assume  a  slightly  higher 
position  than  before.  The  pilot  valve,  of  course,  is  finally  in 
mid-position  just  as  before  the  disturbance.  With  the  pilot 
valve  again  in  mid-position  and  point  (5)  slightly  raised,  the 
governor  G'r  must  assume  a  slightly  higher  position,  so  that 
a  small  positive  static  fluctuation  is  left.  In  this  design,  the 
static  fluctuation  of  the  governor  is  used  to  furnish  stability 
of  regulation,  whereas  relative  displacements  of  points  (3) 
and  (5)  determine  speed  difference  which  finally  establishes 
itself  after  a  disturbance.  For  purposes  of  adjustment,  lever  (4) 
and  the  bracket  supporting  it  are  provided  with  numerous 
holes.  The  connecting  pin  can  be  put  into  any  one  of  these 
holes  so  that  the  fulcrum  can  be  shifted.  With  the  fulcrum 
to  the  left  of  (3),  such  as  at  (2),  the  speed  curve  rises  from  full 
load  to  no  load.  With  the  fulcrum  to  the  right  of  (3),  the 
speed  curve  becomes  reversed.  With  the  fulcrum  at  (3),  the 
governor  is  isochronous. 

Brief  mention  should  be  made  of  the  fact  that  isochronism 
or,  if  desired,  a  reversed  speed  curve,  can  also  be  obtained  by 
letting  the  slowly-yielding  gag  pot  vary  the  ratio  of  speeds 
between  the  prime  mover  and  the  governor. 


The  Double  Relay 

For  close  regulation,  the  governor  traversing  time  and  the 
relay  traversing  time  must  be  small.  To  secure  a  short  travers- 
ing time  for  a  powerful  relay,  the  pilot  valve  (or  equivalent 
releasing  mechanism)  must  be  of  considerable  size.  And  the 
governor  proper  must  be  of  sufficient  size  to  handle  the  pilot 


182    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


valve  quickly.  The  result  is  that  the  commonplace  statements 
about  relay  governing  permitting  the  use  of  very  small  gov- 
ernors are  untrue  for  powerful  relays,  as  many  an  engineer 
has  found  to  his  sorrow. 

This  difficulty  was  overcome  by  the  introduction  of  a  relay 
for  the  relay.  Of  course,  each  relay  must  have  its  return,  so 
that  the  double  relay  becomes  very  complicated  and  "grass- 
hoppery,"  if  both  the  relays  are  returned  by  levers.  External 
complication  is  avoided  by  the  floating  relay  valve  shown  in 
Fig.  122.  If  the  small  central  stem  moves,  ports  in  the  floating 

relay  valve  are  uncovered,  oil  or 
water  pressure  is  admitted  to  one 
end,  and  the  other  end  is  open  to 
exhaust.  The  ports  are  so  ar- 
ranged that  the  floating  (outer) 
valve  promptly  follows  any  move- 
ment of  the  central  stem.  The 
floating  relay  valve  indeed  re- 
moves practically  all  resistance 
from  the  governor,  if  everything 
is  in  working  order.  New  com- 
plications are  introduced,  because 
there  are  more  parts  that  can 
stick  or  bind.  The  ports  of  the 
central  stem  are  so  small  that  scale  or  lint  interferes  with  the 
action.  Water  should  never  be  used  with  the  floating  relay 
valve  ;  nothing  but  pure  oil  is  satisfactory.  In  the  theory  of 
the  double  relay,  an  additional  time  element  enters,  namely 
the  traversing  time  of  the  floating  valve.  The  floating  relay  is 
commonly  used  on  very  large  steam  turbines  and  hydraulic 
turbines.  In  very  large  water  turbines,  a  double  floating  relay 
valve  has  recently  been  introduced. 

A  very  good  diagrammatic  illustration  of  all  the  parts  neces- 
sary for  a  complete  relay  governor  was  given  by  Thoma  in 
Zeitschrift  des  Vereines  Deutscher  Ingenieure,  1912.  This 
illustration  is  here  reproduced  in  Fig.  123.  The  diagram  is  so 
clear  that  very  little  explanation  is  needed.  The  following 
notes  may  be  helpful.  The  centrifugal  governor  (2)  has  no 


Pressure 


Power  Cyl. 
Waste 


FIG.  122 


RELAY  GOVERNING 


183 


collar  or  sleeve,  but  a  spherical  end  bearing  stem.  The  floating 
lever  is  held  in  place  by  a  spring  (1),  so  that  lost  motion  is 
eliminated  even  if  wear  takes  place.  This  arrangement  is  also 
useful  in  avoiding  strain  of  the  mechanism  in  case  the  power- 
control  mechanism  reaches  a  stop  before  the  governor  mechan- 
ism does.  Instead  of  oil-pot  compensation  a  pair  of  friction 
wheels  (3)  is  used  which,  after  a  change  of 'load  has  occurred, 
gradually  returns  the  centrifugal  governor  to  the  same  position 


Connected  to. 
•turbine  gates 


FIG.  123 

and  restores  the  original  speed.  The  friction  wheel  compensator 
is  an  American  invention  and  was  introduced  by  the  Wood- 
ward Governor  Co.  of  Rockford,  111.,  long  ago.  By  means  of 
hand  wheel  (6)  that  position  of  the  governor  which  maintains 
equilibrium  can  be  adjusted,  which  means  that  the  speed  is 
adjusted  by  making  use  of  the  fact  that  the  governor  has  a 
static  fluctuation.  Link  (4)  serves  the  purpose  of  adjusting 
the  speed  and  effectiveness  of  the  return  of  the  pilot  valve  (7), 


184    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

Oil  for  the  power  cylinder  (5)  is  furnished  by  the  gear  pump  (11), 
which  delivers  oil  through  the  overflow  valve  (10)  and  the 
check  valve  (9)  to  air  chamber  (8).  The  overflow  valve  (10) 
is  so  designed  that  the  pump  is  relieved  of  load  as  soon  as  the 
oil  in  the  air  chamber  has  risen  to  a  predetermined  highest 
level. 

References  to  Bibliography  at  end  of  book:   8,  9,  12,  21,  24,  36,  38,  41,  44,  45, 
46,  47,  48,  53,  55,  56,  66,  67,  69,  71,  73,  75,  77,  81. 

3.  Work  Capacity  of  Relay  Governors.  —  The  multi- 
plicity of  designs  of  relay  governors  precludes  a  simple  set  of 
rules  for  the  work  capacity  of  such  governors.  Only  a  few 
guide  posts  can  be  given  here. 

The  largest  direct-control  governor  built  has  a  work  capacity 
of  about  30  ft.  pounds  (for  2%  speed  variation).  Relay 
governors  have  been  built  with  20,000  ft.  pounds  (or  even 
greater)  work  capacity.  Right  here  an  important  difference 
between  the  two  types  of  governors  should  be  mentioned ; 
namely  that  in  direct-control  governing  more  work  may  be 
done  by  the  governor,  if  we  allow  a  greater  speed  variation, 
whereas  in  a  properly  designed  relay  governor  the  speed 
change  has  no  influence  on  the  work  capacity. 

Properly  considered,  the  term  "work  capacity"  is  incom- 
plete, because  it  omits  the  element  of  time.  This  fact  becomes 
manifest  if  we  consider  mechanical  relay  governors  in  which 
the  governor  (measuring  instrument)  throws  in  a  clutch  and 
makes  the  whole  energy  of  the  prime  mover  available  for 
moving  the  energy-controlling  device.  In  such  a  governor  the 
torque  which  can  be  transmitted  to  the  control  is  limited  by  the 
mechanical  strength  of  the  mechanism.  Shafts,  gears,  keys, 
etc.,  must  not  break  under  the  strain  But  work  transmitted 
in  unit  time  equals  torque  times  angular  velocity,  and  total  work 
transmitted  equals  torque  times  angle  passed  over.  Hence, 
the  same  mechanism,  running  at  a  given  rotary  speed,  will 
transmit  more  work,  if  it  is  given  more  time.  But  in  the  govern- 
ing of  hydraulic  turbines  a  comparatively  long  time  is  required 
whenever  the  water  is  supplied  through  a  long  pipe.  This 
condition  is  favorable  to  the  use  of  a  mechanical  governor, 
which  explains  the  fact  that  this  type  of  governor  was  developed 


RELAY  GOVERNING  185 

in  connection  with  hydraulic  turbines  and  is  to-day  limited  to 
such  use. 

In  hydraulic  governors  the  work  capacity  is  the  product 
of  displacement  of  power  cylinder  and  pressure  of  fluid.  If 
water  or  steam  is  used  the  pressure  is  usually  limited  to  that 
of  the  available  supply,  but  if  oil  is  used,  the  pressure  is  de- 
termined solely  by  questions  of  leakage  and  strength  ;  it  often 
equals  200  pounds  per  square  inch.  In  this  definition  of 
work  capacity,  three  features  are  not  included,  namely,  (1) 
detention  by  friction,  (2)  capacity  of  oil  pump,  and  (3)  size 
of  pilot  valve  and  ports.  (1)  Packing  against  high  pressure 
may  produce  great  friction,  particularly  if  cup-leathers  are 
used  in  the  piston.  By  improper  design,  25  %  to  30  %  of  the 
total  force  may  be  absorbed  by  friction.  (2)  The  work  capacity 
of  an  oil-pressure  governor  in  a  given  period  of  time  is  limited 
by  the  capacity  of  the  oil  pump.  If  frequent  and  heavy  changes 
of  load  occur,  a  given  oil  pump  can  serve  a  small  governor  only, 
und,  vice  versa,  a  given  governor  requires  a  large  pump.  But 
in  the  design  of  standard  governors,  or  even  of  a  given  governor 
for  a  given  purpose,  the  frequency  and  amount  of  load  changes 
r.re  unknown.  Hence  it  has  become  customary  to  make  the 
displacement  per  minute  of  the  oil  pump  equal  to  5  to  10  times 
the  displacement  of  the  power  cylinder  per  stroke.  The  pump 
cperates  all  the  time.  The  excess  passes  off  through  a  spring- 
loaded  relief  valve  and  is  returned  to  the  pump  inlet.  In  a 
Swiss  design,  the  pilot  valve  has  negative  lap,  which  means 
that  the  valve  is  open  in  mid-position.  The  oil  can  flow  through 
the  open  valve.  In  centrifugal  governors,  the  oil  pump  is 
usually  a  gear  pump  and  is  arranged  at  the  bottom  of  the 
governor  spindle  (see  Fig.  124).  (3)  The  size  of  the  pilot  valves 
and  of  the  ports  in  a  hydraulic  governor  has  no  influence  on 
the  total  work  capacity,  but  has  a  very  marked  influence  on 
the  work  capacity  in  unit  time  and  on  the  relay  traversing  time. 
The  larger  the  pilot  valves  and  ports,  the  shorter  the  relay 
traversing  time,  Tr.  It  will  be  proved  that,  for  closest  regula- 
tion, Tr  must  be  small,  which  means  large  pilot  valves.  But 
large  pilot  valves  offer  considerable  resistance  to  the  governor. 
The  operating  fluid  exerts  a  dynamic  thrust  on  the  edges  of 


186    GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 


Governor 
Spindle 


Drivinq 
Shaft 


the  pilot  valve,  and,  besides,  the  danger  from  sticking  due  to 
one-sided  pressure  and  unequal  expansion  grows  with  the  size 

of  the  pilot  valve.  For 
this  reason  the  diameter 
of  the  latter  never  exceeds 
one-fourth  of  the  diameter 
of  the  power  piston,  and 
occasionally  goes  down  to 
one-tenth  of  that  diame- 
ter. The  diameter  of  a 
floating  relay  valve  may 
go  up  to  one-third  of  that 
of  the  power  cylinder,  or 
even  more. 

It  should  be  remem- 
bered that  the  resistance 
to  motion  offered  by  the 
pilot  valve  (or  clutch,  or 
other  force-releasing  me- 
Oil  Punnp  chanism)  is  a  load  on  the 
governor  (measuring  in- 
strument), which  requires  a  change  of  speed,  before  motion  of 
the  pilot  valve  can  begin  (see  paragraph  5  of  Chapter  II,  on 
overcoming  passive  resistance).  In  relay  governing,  the  pilot 
valve  is  part  of  the  governor,  and  its  frictional  resistance  becomes 
part  of  the  internal  friction  of  the  governor. 

References  to  Bibliography  at  end  of  book:   8,  9,  12,  36,  38,  41,  66,  60,  66,  67, 
69,  73. 

4.  Speed  Fluctuations.  —  A  complete  theory  of  relay  gov- 
erning is  very  complex.  The  most  ambitious  attempt  at  a 
solution  was  made  by  Professor  Stodola  and  was  published 
in  the  Schweizerische  Bauzeitung,  1893  and  1894.  Professor 
Stodola  considers  the  action  of  the  water  in  long-pipe  lines,  and 
even  introduces  the  action  of  surge  tanks  with  compressed 
air.  He  gets  a  linear  differential  equation  of  the  7th  order,  and, 
by  means  of  a  determinant,  derives  stability  relations.  While 
his  work  deserves  to  be  better  known,  it  exceeds  the  limits  of 
this  volume. 


FIG.  124 


RELAY   GOVERNING 


187 


However,  a  fair  knowledge  of  the  influence  of  the  funda- 
mental quantities  on  the  process  of  regulation  may  be  gained 
from  the  following  simplified  treatment. 

The  statement  was  made  in  the  description  of  types  of  relay 
governors  that,  with  proper  design,  the  utilized  travel  of  the 
governor  could  be  made  very  small,  so  small  that  the  mass  of 
the  governor  becomes  almost  negligible.  The  simplified  theory 
in  question  neglects  the  mass  of  the  governor  entirely,  or,  if 
the  governor  has  mass,  assumes  that  the  natural  period  of 


No  Load 

New  Torque 

Old  Torque 

Full  Load 


-f — No  Load.CciseZ 


..__^-_-» Mew  Torque  Cose? 


FullLoadl.CaseZ 


FIG.  125 

vibration  of  the  governor  is  very  small  compared  to  the  relay 
traversing  time. 

The  second  assumption  is  that  the  speed  of  the  relay 
mechanism  or  power  mechanism  is  constant.  This  is  very 
nearly  so  in  mechanical  relay  governors,  and  is  true  in  hydraulic 
governors  whenever  the  pilot  valve  is  wide  open. 

The  usual  assumptions  about  linear  relations  between  speed 
and  governor  position,  and  between  governor  position  and 
torque  are  likewise  made  here. 

In  Fig.  125,  the  abscissae  represent  time.  The  ordinates 
represent  two  different  quantities,  namely  (1)  relay  position 


188    GOVERNORS  AND  THE  GOVERNING   OF   PRIME   MOVERS 

(which  also  indicates  position  of  power  control),  and  (2)  speed 
of  governor  or  of  prime  mover.  The  speed  curve  can  be  used 
for  both  governor  and  prime  mover  if  we  let  it  represent  the 
ratio  of  actual  speed  to  average  speed  ;  for  this  ratio  the  letter 
U  has  been  used.  At  time  (3)  let  the  torque  suddenly  be 
changed  from  "old  torque"  to  "  new  torque."  Then  the 
torque  (2)  (3)  is  unbalanced  and  causes  a  change  of  speed,  the 
rate  of  which  is  given  by  the  equation 

du_  M        dM_      M_      dU      J_ 
~dt  =:  T  °r  ~udt  =  I  u  °     dt     =  ~Ts 

where  U  is  the  relative  speed  change,  and  where  Ts  is  the 
starting  time  of  the  prime  mover  (compare  paragraph  2  of 
Chapter  IX).  In  the  illustration,  the  straight  line  (8)  (9) 
represents  this  rate  of  change  of  speed.  The  latter  sets  the 
governor  and  relay  in  motion.  According  to  the  assumptions 
of  the  present  elementary  theory,  the  rate  of  motion  of  the  relay 
is  constant.  It  traverses  the  whole  range  from  full  load  to  no 
load  in  the  "relay  traversing  time"  Tr.  Hence  the  straight 
line  (1)  (12)  indicates  the  rate  of  change  of  position  of  the 
power-controlling  mechanism.  Evidently  the  unbalanced  torque 
decreases  on  the  way  from  point  (2)  to  point  (4),  and  vanishes 
at  the  latter  place.  But  unbalanced  torque  causes  change  of 
speed  and  is  proportional  to  the  rate  of  change.  Hence,  the 
curve  of  speed  must  have  a  horizontal  tangent  vertically  above 
point  (4).  From  mathematics  it  is  known  that  a  curve  the 
tangent  of  which  changes  proportionally  to  the  change  of  ab- 
scissae is  a  parabola  ;  but  that  is  the  case  with  the  speed  curve 
(3)  (8)  (10),  in  question,  which  may,  therefore,  be  called  the 
parabola  of  speed  deviation.  To  the  right  of  (10),  the  speed 
drops,  because  the  unbalanced  torque  is  negative.  For  the 
sake  of  a  lucid  graphical  representation,  the  scale  for  the  speed 
curve  and  the  scale  for  the  change  of  torque  should  be  so  coor- 
dinated that  the  distance  (6)  (12)  represents  the  static  fluc- 
tuation if  measured  with  the  speed  scale.  If  the  scales  are 
chosen  in  this  manner,  the  straight  line  (1)  (12)  represents  not 
only  position  of  relay,  but  also  equilibrium  speed  of  governor. 
The  governor  passes  through  an  equilibrium  position  at  the 


RELAY  GOVERNING  .        189 

intersection  of  the  straight  line  (1)(12),  with  the  parabola  of 
speed  deviation  (see  point  (5)).  The  governor  and  relay 
reverse  themselves,  and  a  new  branch  of  the  parabola  is  started. 
No  matter  how  many  branches  of  the  parabola  there  are,  they 
are  all  parts  of  the  same  parabola,  because  the  latter  is  de- 
termined solely  by  T  s  and  Tr,  and  both  of  these  quantities  are 
constant.  Straight  line  (5)  (7)  has  negatively  the  same  slope 
as  line  (1)(12).  If  it  be  extended  to  the  left  to  point  (8) 
(intersection  with  parabola),  the  two  parabola  sections  (8) 
(11)  (5)  and  (5)  (7)  are  identical.  The  same  is  true  for  the  next 
branch  of  the  parabola,  so  that  the  total  number  of  waves  can 
easily  be  found  by  drawing  the  zigzag  line  (3)  (5)  (8)  (11),  etc., 
in  the  first  parabola. 

The  speed  change   (13)  (10)  can  be  expressed  by  a  simpb 
formula.     Let  Z  be  the  relative  load   change,  or  the  ratio 

load  change  (0)  (3) 

.      ,,  which  means  Z=  //>W^N,  then  time  (2)  (4)  =  ZTr, 
maximum  load  (6)  (12) 

and  unbalanced  torque  at  beginning  of  disturbance  equals  ZM  m  ; 
if  this  latter  torque  acted  during  the  whole  time  Tr,  the  speed 

change  would  be  Du  =  —  j-^ZTr  and  the  relative  speed  change 

Mm          Tr 

would  be  U  =  Z2Tr-^  =  Z2-^.      But    the   unbalanced   torque 
J.  u  j.  a 

drops  off,  and  the  speed  curve  follows  parabola  (3)  (8)  (10) 
instead  of  straight  line  (3)  (9)  .  From  a  well-known  property 
of  the  parabola,  (13)  (10)  equals  one  half  of  (13)  (9),  so  that 
the  actual  relative  speed  change  is  found  from 


If,  for  instance,  the  relay  time  is  two  seconds  and  the  starting 
time  equals  10  seconds,  then  for  50%  load  change  we  have 


It  is  interesting  to  note  that  the  static  fluctuation  of  the 
governor  and  relay  mechanism  does  not  appear  in  this  equa- 


190    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

tion  (1).  In  this  respect,  relay  governing  with  constant  speed 
of  relay  mechanism  differs  radically  from  direct-control 
governing. 

Yet  it  stands  to  reason  that  the  static  fluctuation  which, 
'to  a  certain  extent,  is  a  measure  of  the  stability  of  the  system, 
will  have  some  influence  on  the  process  of  regulation.  In  the 
diagram  (Fig.  125)  this  influence  appears  as  follows :  The 
scales  for  torque  and  for  speed  were  so  selected  that  (6)  (12) 
represents  both  full  load  torque,  and  p,  where  p  is  the  static 
fluctuation.  Therefore,  if  p  is  changed,  one  of  the  two  scales 
must  be  changed,  and  since  a  straight  line  is  more  easily  changed 
than  a  parabola,  the  scale  for  speed  is  left  unchanged,  which 
means  that  we  must  change  the  scale  for  torque.  In  conse- 
quence, inclination  of  line  (1)  (12}  will  vary  with  the  variation 
of  static  fluctuation  p.  If  p  is  very  small,  then  a  very  small 
change  of  speed  will  move  the  governor  through  the  whole  range 
of  adjustment.  In  Fig.  125  a  regulation  diagram  for  a  greater 
static  fluctuation  has  been  sketched  in  dotted  lines.  Evidently, 
the  first  wave  remains  just  as  it  was  before,  but  the  regulation 
is  completed  in  less  time.  For  governors  working  with  a  con- 
stant speed  of  relay  (mechanical  governors),  a  great  static 
fluctuation  is  advantageous. 

The  regulation  diagram,  Fig.  12,5,  is  particularly  useful 
for  impressing  upon  engineers  the  very  harmful  influence  of 
friction  in  the  governor  and  of  lost  motion  in  the  relay  mechan- 
ism. The  effects  of  governor  friction  are  illustrated  in  the  dia- 
gram Fig.  126,  which  is  of  the  same  type  as  Fig.  125.  Since 
it  is  rather  difficult  to  see  before  the  mind's  eye  the  connection 
between  the  diagram  and  the  governor  mechanism,  a  constant 
speed  relay  has  been  shown  in  Fig.  127  for  the  purpose  of  sup- 
plementing Fig.  126.  If  in  Fig.  127  the  speed  grows,  the 
governor  rises,  making  electric  contact  with  the  upper  one  of 
two  contacts.  Wires  and  control  switches  are  provided  for 
starting  an  electric  motor  in  the  proper  direction  to  reduce  the 
supply  of  energy.  By  the  movement  of  the  motor  the  electric 
contact  is  broken,  unless  the  governor  keeps  on  going  with  a 
speed  as  great  as  (or  greater  than)  that  of  the  relay.  The 
moving  of  the  contacts  by  the  motor  constitutes  the  return. 


RELAY  GOVERNING 


191 


During  the  process  of  regulation,  the  governor  will  go  ahead  of 
the  relay,  and  we  will  assume  here  that  it  can  do  so  by  virtue 
of  the  contacts  being  slip  contacts  or  mercury  dip  contacts. 


More 
Power 


Electric 
Motor 


Less  Power 


FIG.  126 

By  making  this  assumption  we  make  the  present  study  applic- 
able to  the  hydraulic  relay  in  which  the  pilot  valve  can  likewise 
overtravel  and  can  go  ahead  of  the  relay.  Attention  is  again 
called  to  the  assumption  that  the  governor  is  practically  mass- 
less,  which  means  that  its  natural 
period  of  vibration  is  very  small 
compared  to  the  relay  traversing 
time. 

If  there  is  friction  in  the 
governor,  the  angular  velocity 
must  grow  by  Du  =  \  qu  (see 
paragraph  4  of  Chapter  II)  be- 
fore the  governor  begins  to  move. 
This  phase  of  the  regulating  pro- 
cess is  represented  by  the 
straight  line  (1)  (2),  because 
during  the  time  (1)  (3)  the  un- 
balanced torque  is  constant  and 
equal  to  the  difference  (old  torque  minus  new  torque).  From  point 
(2)  on,  the  speed  curve  is  parabolic,  just  as  before. 

The  governor  displacement  lags  behind  the  motion  of  a 
frictionless  governor,  as  indicated  by  the  difference  between 


FIG.  127 


192    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

the  speed  curve  (which  also  represents  position  of  frictionless 
governor)  and  the  dotted  parabola  (5)  (4),  which  represents 
the  actual  motion  of  the  governor.  At  point  (4)  the  governor 
stops  ;  it  remains  motionless  until  the  speed  has  dropped  \qu 
below  the  equilibrium  speed  belonging  to  the  position  of  point 
(4),  which  occurs  at  point  (5).  The  governor  changes  contacts 
as  soon  as  the  upward  motion  of  the  contacts  and  the  down- 
ward motion  of  the  governor  intersect,  which  occurs  at  point 
(6).  The  relay  (in  this  case  the  electric  motor)  reverses  and 
continues  in  its  new  direction  until,  in  the  diagram,  the  straight 
line  representing  its  motion  drops  %q  below  the  speed  parab- 
ola, see  points  (7)  and  (8).  Again,  the  governor  is  reversed, 
and  so  forth.  It  is  evident  that  the  governor  never  comes  to 
rest.  The  tangent  points  of  two  successive  parabola  branches 
move  closer  and  closer  to  the  line  (12)  (11}  representing  the 
new  torque.  As  soon  as  the  tangent  points  fall  on  this  line, 
the  reverse  of  'the  relay  occurs  simultaneously  with  the  inflexion 
points  of  the  parabola.  All  following  parabola  branches  are 
alike. 

From  the  diagram,  Fig.  126,  it  is  clear  that  the  remaining 
speed  fluctuation  is  greater  than  q,  the  detention  by  friction. 
Distance  (1)  (2)  =  (9)  (10)  represents  not  only  %q  but  also 
that  fraction  of  the  total  torque  which  is  unbalanced  when  the 
parabola  intersects  line  (12)  (11),  but  since  the  whole  torque 
corresponds  to  a  speed  deviation  p  (static  fluctuation),  the 

-a 
unbalanced   torque  ratio  is   Z  .=  —  .     From   equation    (1)  we 


l/i  q\2  y 

find  the  corresponding  speed  deviation  to  be  U  =  -(--]  —  ^  to 

2\  p_J   1  s 

either  side,  which  means  a  total  speed  fluctuation  of  U  due  to 
friction  of 


Let    T8  =  8    sec.,    Tr  =  1.5    sec.,    p  =  2%,    q  =  1  %,    then    Uf 
1\2  1.5 

T=  L17%;    for  q  =  2%>    U'  would  be  almost    4f%. 

The  influence  of  friction  grows  with  the  square  in  this  type  of 
regulation. 


RELAY    GOVERNING 


193 


The  harmful  effect  of  friction  is  very  much  reduced,  if  the 
governor  is  prevented  from  going  ahead  of  the  relay.  This 
favorable  condition  can.be  obtained  in  Fig.  127  by  letting  con- 
tact tongue  (1)  fit  between  the  relay  contacts  so  that  it  abuts 
and  presses  against  one  or  the  other. 

The  same  harmful  effect  which  is  caused  by  friction  in  the 
governor  is  also  produced  by  several  other  resistances.  Evi- 
dently, any  force  which  must  be  exerted  by  the  governor  to 
release  the  action  of  the  relay  mechanism  requires  a  speed 
difference  of  the  sort  indicated  in  Fig.  126.  Such  a  force  must 
be  exerted,  if  the  pilot  valve  in  hydraulic  relay  governors 
moves  hard  (for  instance  by  being  forced  to  one  side  through 
imperfections  in  workmanship).  Such  a  force  must  also  be 


FIG.  128 

exerted  in  mechanical  relays  to  keep  the  clutch  engaged,  etc. 
A  very  similar,  although  not  strictly  identical,  effect  is  produced 
in  hydraulic  relays  by  lap  of  the  pilot  valve  and  by  excessive 
clearance  of  the  pilot  valve  in  its  bushing.  Lost  motion  in 
the  joints  of  the  relay  mechanism  has  an  effect  which  is  similar 
in  one  respect  and  different  in  another.  Inasmuch  as  the 
governor  has  to  travel  a  certain  distance  to  take  up  lost  motion, 
the  problem  resembles  that  covered  by  Fig.  126  ;  but  inasmuch 
as  time  is  lost  in  the  return  by  the  power  part  of  the  relay, 
the  problem  differs.  The  effect  of  time  lag  in  the  mechanism 
is  commonly  explained  by  the  method  shown  in  Fig.  128. 
The  diagram  is  so  similar  to  Fig.  126  that  no  explanation  is 
needed  except  this:  At  point  (1)  the  governor  does  not  reverse 
the  relay  ;  the  reversal  occurs  after  the  lost  time  TI,  that  is 


194    GOVERNORS  AND  THE   GOVERNING  OF  PRIME  MOVERS 


to  say  at  point  (2).  The  same  action  occurs  at  points  (3) 
and  (4),  (5)  and  (6),  (7)  and  (8),  etc.  The  process  is  drawn 
out  longer  than  it  would  be  without  time  loss,  but  it  finally 
ends  without  lasting  vibration.  For  practical  application  it 
should  be  remembered,  however,  that  lost  motion  involves  the 
features  of  both  Fig.  126  and  Fig.  128,  so  that  lost  motion,  as 
a  rule,  results  in  never-ending  speed  fluctuations  of  small 
amplitude. 

In  many  relay  governors,  particularly  in  those  of  the 
hydraulic  type,  the  velocity  of  " opening"  and  " closing"  is 
not  constant,  but  grows  with  the  relative  displacement  of  gov- 
ernor and  piston  in  power  cylinder.  The  regulation  diagram 
then  looks  somewhat  like  Fig.  129.  The  slope  of  the  power- 
piston  velocity  curve  varies  with 
the  lengths  of  the  intercepts  be- 
tween the  two  curves.  For  those 
who  are  mathematically  inclined, 
it  may  be  remarked  that  the 
assumption  of  proportionality 
between  slope  and  intercept  leads 
to  a  very  interesting  theory  of 
relay  governing.  It  will  be  ex- 
plained in  the  author's  book  on 
advanced  theory  and  practice  of 
prime-mover  governing.  For  the  purposes  of  the  present  rather 
elementary  theory  we  replace  the  curve  (1)  (3)  (5)  of  Fig.  129  by 
the  broken  line  (!)(&)  (8)  (4)  (6).  The  speed  curve  then  is 
resolved  into  a  succession  of  straight  lines,  such  as  (1)(6)  and 
(7)  (5),  and  parabolas,  such  as  (6)  (7).  The  diagram  is  identical 
with  Fig.  128,  and  the  greatest  speed  fluctuation  is  easily  found 
by  graphical  construction. 

References  to  Bibliography  at  end  of  book:  8,  9,  10,  12,  16,  20,  21,  36,  38,  41, 
47,  56,  66,  67,  69,  73,  78,  82,  83. 


Position 
of  Power 
Mechcrnism 


CHAPTER  XIV 

GOVERNOR  TROUBLES  AND  THEIR  REMEDIES 

WHILE  the  principles  which  underlie  all  cures  for  governor 
troubles  are  clearly  indicated  in  the  foregoing  chapters,  the 
principal  troubles,  their  causes  and  remedies,  are  dealt  with 
here  for  the  benefit  of  the  operating  engineer. 

1.  Regulation  is  not  Close  Enough.  —  There  is  too  much 
speed  difference    (pressure   difference,  rate  of  flow  difference) 
between  full  load  and  no  load. 

Several  methods  are  open  to  make  regulation  closer.  A 
smaller  portion  of  the  travel  of  the  governor  may  be  utilized 
for  the  whole  range  from  full  load  to  no  load,  or  the  governor 
proper  may  be  altered.  If  it  is  of  the  spring-loaded  type,  regu- 
lation is  made  closer  by  using  a  softer  (more  flexible)  spring. 
In  a  helical  spring  use  more  coils,  or  thinner  wire,  or  grind  off 
the  outer  layers  of  the  spring  (reduce  its  diameter).  In  leaf 
springs  grind  some  off  the  width  of  the  spring.  If  the  spring 
acts  on  a  lever,  reduce  the  length  of  the  latter  and  tighten 
spring. 

All  of  these  changes  reduce  the  static  fluctuation  of  the 
governor.  The  latter  (for  a  given  prime  mover  and  governor) 
must  not  be  reduced  beyond  a  certain  limit  which  is  set  partly 
by  the  design  of  the  governor  and  partly  by  that  of  the  prime 
mover  (see  paragraph  2  of  Chapter  IX).  If  further  reduction 
of  the  static  fluctuation  is  desired,  the  flywheel  effect  must  be 
increased,  or  a  prompter  governor  must  be  used,  or  else  tan- 
gential inertia  must  be  used,  or  finally  a  compensating  oil  pot 
may  be  applied.  For  all  of  these,  see  paragraph  2  of  Chapter  IX. 

2.  Racing. —  Two  broad  classes  must  be  distinguished  : 

(a)  Racing  which  appears  from  the  very  beginning  of  the 
operation,  that  is,  with  a  new  machine  ; 

(b)  Racing  which  appears  after  the  machine  has  been  in 
operation  several  months  or  years. 

195 


196     GOVERNORS  AND   THE   GOVERNING   OF  PRIME   MOVERS 

Racing  which  appears  after  the  machine  has  been  in 
operation  several  months  or  years 

Discussing  this  latter  case  first,  we  find  that  racing  may 
gradually  develop  from  several  causes  : 

First,  the  oil  may  leak  out  of  the  gag  pot,  or  may  be  pumped 
out  of  it  by  quick  motion  of  the  governor.  Refill  oil  pot  and 
make  such  changes  in  its  design  that  emptying  during  regular 
operation  becomes  impossible  (see  paragraph  2  of  Chapter  IX). 
The  adjustable  passage  for  oil  may  be  too  large,  or  the  oil 
may  be  too  light.  In  governors  with  compensating  oil  pot 
(paragraph  2  of  Chapter  IX,  paragraph  2  of  Chapter  XIII) 
too  free  an  opening  of  the  oil  pot  will  likewise  cause  racing.  The 
same  result  is  produced  by  air  entering  the  gag  pot  with  the 
oil. 

A  second  reason  for  racing  (or  running  away  akin  to  racing) 
results  from  such  changes  in  the  transmitting  linkage  between 
governor  and  power-control  mechanism  l  as  do  not  sufficiently 
shut  off  the  supply  of  energy  near  or  at  the  no-load  position. 
Racing  due  to  this  cause  occurs  only  if  the  load  is  very  light. 
Obviously,  proper  change  in  the  linkage  will  cure  this  condition. 

A  third  reason  for  racing  (and  a  very  prolific  one)  is  friction, 
either  in  the  governor  or  in  the  valve  gear  (paragraph  4  of 
Chapter  II,  5  of  Chapter  II,  3  of  Chapter  XIII).  To  ascertain 
whether  or  not  friction  is  responsible  for  the  trouble,  jiggle  or 
pump  the  governor  up  and  down  by  hand,  taking  great  care 
that  the  upward  and  downward  thrust  exerted  on  the  governor 
are  alike.  This  eliminates  friction  (paragraph  4  of  Chapter  II, 
2  of  Chapter  VIII,  4  of  Chapter  IX)  and  stops  racing,  if  the 
latter  be  due  to  friction  in  the  governor  or  power-control 
mechanism  (in  the  case  of  direct-control  governing)  or  due  to 
friction  in  the  governor  proper,  in  the  case  of  relay  governing. 

Pumping  the  governor  will  not  always  eliminate  frictional 
speed  fluctuation  (or  pressure  fluctuation,  or  delivery  fluctua- 
tion in  other  forms  of  governors),  in  the  case  of  relay  governors, 
because  there  may  be  friction  in  the  relay  or  in  the  power-con- 

1  Misadjustments  of  this  sort  frequently  occur  in  the  wake  of  valve  adjustments 
and  repairs. 


GOVERNOR   TROUBLES  AND   THEIR  REMEDIES  197 

trol  mechanism.  To  discover  such  friction,  try  to  move  the 
latter  mechanism  by  hand  or  by  a  lever  in  the  direction  of 
least  resistance  (care  being  taken  not  to  overstrain  the  mechan- 
ism). If  doing  so  stops  the  speed  fluctuation,  the  frictional 
'resistance  is  too  great  for  the  available  relay  force,  or  the 
available  force  has  become  less  (see  also  under  leakage).  In 
this  case  the  frictional  resisting  force  should  be  measured. 
The  remedy  consists,  of  course,  in  removing  the  undue  friction. 
The  causes  for  a  gradual  or  for  a  sudden  rise  of  friction  are  so 
manifold  that  they  cannot  all  be  enumerated  here.  Among 
them  are  :  gumming  of  valves  or  valve  stems  due  to  improper 
oil ;  sticking  of  valve  stems  due  to  solid  matter  in  steam ; 
lack  of  lubrication  ;  deposit  of  tar  (in  regulating  valves  of  gas 
engines)  ;  wearing  of  knife  edges  ;  binding  due  to  lack  of  align- 
ment ;  and  others.  It  occasionally  requires  very  patient  study 
to  hunt  down  and  locate  the  spot  where  the  undue  friction 
occurs. 

A  fourth  reason  is  leakage  in  the  pilot  valve  in  hydraulic 
relay  governors.  Placing  of  pressure  gauges  at  both  ends  of 
the  power  cylinder  is  a  good  means  for  judging  whether  or  not 
leakage  is  responsible  for  the  trouble.  If  it  is,  a  new  pilot  valve 
and  bushing  are  needed.  In  oil-pressure  governors  the  oil 
pump  may  be  worn  out  or  deranged. 

A  fifth  reason  is  lost  motion  in  the  relay  mechanism  (para- 
graph 4  of  Chapter  XIII) .  A  weak  spring  or  a  weight  keeping 
the  parts  always  in  contact  in  the  same  direction  will  eliminate 
the  influence  of  lost  motion  (see  (1),  Fig.  123),  and  will,  inci- 
dentally, indicate  whether  or  not  lost  motion  is  responsible  for 
the  racing. 

A  sixth  reason  is  the  dulling  of  knife  edges  in  the  releasing 
gear  of  steam  engines.  At  the  right  cut-off  the  dulled  edges 
slip  so  that  alternately  too  much  and  not  enough  steam  is 
admitted.  The  remedy  is  plain. 

A  seventh  reason  is  found  likewise  in  releasing  gears  and 
more  particularly  in  those  which  depend  upon  a  partial  vacuum 
in  a  dashpot  for  closing  the  valve.  If  the  dashpots  are  worn 
or  improperly  adjusted,  anything  from  scarcely  perceptible 
racing  up  to  disastrous  running  away  of  the  engine  may  occur. 


198    GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

To  tell  whether  racing  or  overspeeding  is  caused  by  dashpot 
trouble,  tie  a  very  long,  flexible  spring  to  the  dashpot  arms  so 
that  the  spring  assists  the  dashpot  in  closing  the  valve.  Make 
the  force  of  the  spring  in  pounds  approximately  equal  to  5  to  7 
times  the  area  of  the  vacuum  pot  in  square  inches.  If  the 
irregular  speed  was  due  to  vacuum  pot  trouble,  the  spring  will 
cure  it.  Of  course,  the  spring  looks  like  an  afterthought,  so 
that  the  vacuum  pot  should  be  renewed. 

An  eighth  reason  is  frequently  found  when  the  governor  is 
belt  driven.  It  consists  in  a  belt  which  slips  at  intervals. 
Application  of  a  belt  tightener  will  soon  tell  whether  or  not  the 
belt  is  responsible  for  the  trouble. 

A  ninth  reason  appears  whenever  springs  are  tightened  or 
weights  are  added  for  the  purpose  of  increasing  the  speed  of 
the  prime  mover,  unless  the  governor  is  so  designed  that  the 
speed  can  be  increased  without  variation  of  stability  (see 
Chapter  V).  Increase  the  stiffness  of  the  adjusting  spring  (by 
using  fewer  coils)  or  increase  its  lever  arm,  or  (in  the  case  of 
shifting  a  weight)  put  a  spring  into  the  oil  pot.  Every  one  of 
these  means  restores  the  stability  (and  static  fluctuation) 
which  was  lost  by  the  previous  adjustment. 

Racing  which  appears  immediately  after  the  installation 
of  the  prime  mover 

Any  of  the  reasons  which  produce  racing  in  an  old  prime 
mover  will,  of  course,  have  the  same  action  in  a  new  prime 
mover.  But  there  exist  other  causes  which  will  produce  fluc- 
tuations at  once,  and  which,  once  removed,  will  not  return. 
They  will  now  be  enumerated. 

In  order  to  tell  the  source  of  the  trouble,  observe  whether 
the  racing  occurs  at  all  loads  or  whether  it  occurs  only  at 
certain  loads  (for  instance,  near  the  no-load  position). 

If  the  racing  occurs  at  all  loads,  and  if  none  of  the  causes 
before  given  exist,  then  the  static  fluctuation  is  too  small 
(paragraph  2  of  Chapter  IX),  or  there  is  not  enough  damping 
(by  friction  or  oil  gag  pot) .  If  permissible,  the  static  fluctuation 
should  be  increased,  but  this  measure,  of  course,  increases  the 


GOVERNOR  TROUBLES  AND  THEIR  REMEDIES  199 

speed  (respectively  pressure,  or  delivery)  difference  between 
full  load  and  no  load.  If  permissible,  the  oil  pot  should  be 
made  more  effective,  either  by  adjustment,  or  by  a  larger  pot, 
if  close  adjustment  overheats  the  oil.  Again,  more  effective 
damping  by  oil  pot  increases  speed  fluctuations  whenever  the 
load  changes.  In  that  case  racing  can  only  be  cured  by  more 
inertia  in  the  prime  mover  (heavier  flywheel)  or  by  a  prompter 
governor  (smaller  traversing  time,  Chapter  IV,  paragraph  2 
of  Chapter  IX).  If  temporary  speed  fluctuation  after  a  change 
of  load  is  permissible,  racing  can  be  cured  by  a  compensating 
dashpot,  or  similar  arrangement  (see  paragraph  2  of  Chapter 
IX  —  Bee  governor,  Chorlton-Whitehead  governor,  Armstrong 
governor,  also  figures  120,  121,  123).  This  type  of  governor 
and  oil  pot  deserves  to  be  more  widely  used  than  it  now  is. 
Use  of  tangential  inertia  in  governors  also  cures  racing,  but  can 
be  recommended  for  shaft  governors  only  (see  paragraph  3  of 
Chapter  IX)  ;  and  even  there  it  is  sometimes  of  doubtful  value. 

In  relay  governors  racing  is  caused  by  absence  of  a  return 
in  the  governor  mechanism  (see  paragraph  2  of  Chapter  XIII). 
Study  of  the  governor  will  immediately  tell  whether  a  return 
(compensator,  anti-racing  device)  has  been  provided.  The 
pilot  valve,  or  other  relay,  must  be  returned  to  make  the 
governor  satisfactory. 

If  racing  or  speed  fluctuations  occur  in  one  certain  position 
of  the  governor  and  valve  gear,  one  of  two  causes  is  present  (in 
the  case  of  speed  governing) .  Either  the  power-control  mechan- 
ism does  not  vary  the  supply  of  energy  uniformly  with  the 
travel  of  the  governor,  reducing  stability  to  an  unpermissibly 
small  amount  in  one  spot  (paragraph  2  of  Chapter  IX)  or  else 
the  power-control  mechanism  reacts  in  certain  positions  upon 
the  governor  in  such  a  way  as  to  reduce  the  stability  or  to  remove 
it  altogether  (see  paragraph  3  of  Chapter  III). 

The  first  case  is  very  common  in  governors  operating  a 
throttle,  either  for  steam  in  steam  engines  or  turbines,  or  for 
air  and  gas  in  internal  combustion  engines.  When  a  throttle 
is  just  cracked,  a  small  increase  of  area  changes  the  flow  through 
the  valve  very  much  more  than  when  it  is  almost  wide  open 
(see  Fig.  130).  The  curve  in  this  illustration  shows  the  general 


200    GOVERNORS  AND  THE  GOVERNING  OF   PRIME   MOVERS 


<u 

4-v+-   £   o 

Pressure  Ratio  = 
Pressure  bevond  Ihrott 

I|l£ 

£  £  0^5 
0        0  r 

/^ 

Pressure  ahead 
(on  the  basis  thai 
steam  flow  is  pr 
to  pressure  beyo 

f 

7 

/ 

5 

FIG.  130 


trend  only,  because  the  curves  differ  a  little  for  wet  steam,  dry 

steam,   air,   and  for  different  gases.     However,   the   curve  is 

given,  solely  for  the  purpose  of  pointing  out  that  there  must 

j^  be  a  variable-rate  linkage  or  a 

cam  interposed  between  governor 
and  throttle  if  there  is  to  be 
constant  stability  over  the  whole 
range  from  full  load  to  no  load, 
unless  the  governor  is  designed 
with  variable  stability  in  such  a 
way  as  just  to  counteract  the 
action  of  the  throttle.  The  vari- 
ability of  the  rate  of  flow  through 
a  throttle  in  different  stages  of 
opening  is  one  of  the  most  fruit- 
ful sources  from  which  poor  governing  springs.  And  the  source 
seemingly  never  dries  up. 

The  second  case,  namely  reaction  by  the  valve  gear  in 
certain  positions  (paragraph  3  of  Chapter  III)  should  really 
not  exist,  because  it  is  usually  due  to  lack  of  foresight  or  lack 
of  knowledge  on  the  part  of  the  designer.  If  it  does  exist  either 
near  the  full-load  or  near  the  no-load  position,  it  can  be  cured 
by  an  auxiliary  spring  which 
enters  into  action  at  one  end 
of  the  governor  travel  only. 
Such  a  spring  is  diagram- 
matically  shown  in  Fig.  131, 
where  it  enters  into  action 
near  the  no-load  position. 
The  spring  can,  of  course, 
be  so  placed  as  to  enter  into 
action  at  the  full-load  posi- 
tion. It  can  also-  be  placed 
out  of  sight  in  the  oil  gag  FlG-  131 

pot.  To  do  so  is  a  favorite  trick  of  skilled  erecting  engineers, 
because  it  gets  away  from  the  criticism  that  the  spring  is  an 
afterthought. 

Racing  at  light  loads  occurs  in  most  centrifugal  pumps  and 


GOVERNOR  TROUBLES  AND  THEIR   REMEDIES  201 

centrifugal  blowers.  The  surest  remedy  is  to  increase  the 
load,  for  instance  by  opening  a  by-pass  from  discharge  to  suc- 
tion. Properly  designed  governors  for  turbo-pumps  and  turbo- 
blowers automatically  take  care  of  this  feature  (Chapters  XI 
and  XII). 

3.   Speed  Fluctuation   is   too   great,  when   load   changes 
suddenly.  --  This   may  be   due  to   any  one  of  many  causes, 
•  the  principal  ones  of  which  are  given  below. 

First,  there  is  too  much  energy  stored  up  in  prime  mover 
beyond  control  of  the  governor.  No  adjustment  in  existence 
will  improve  this  condition.  It  means  a  rebuilding  of  the 
prime  mover,  or  an  additional  power-control  mechanism,  for 
instance  on  the  exhaust,  and  so  designed  that  it  enters  into 
action  temporarily  for  great  and  sudden  changes  of  load. 
This  condition  is  almost  invariably  a  sign  of  poor  and  thought- 
less design  (see  paragraph  5  of  Chapter  IX).  Final  judgment  as 
to  whether  or  not  stored  up  energy  beyond  control  of  the  gov- 
ernor is  responsible  for  excessive  speed  fluctuation  requires  study 
of  the  engine  or  turbine  and  calculation  of  the  volumes  in  which 
steam  under  pressure,  or  explosive  mixture,  etc.,  is  stored. 

Second,  there  is  not  enough  flywheel  effect  in  the  prime 
mover.  The  decision  whether  or  not  defective  regulation  is 
due  to  this  cause  is  usually  quite  difficult,  because  addition  of 
flywheel  effect  always  improves  speed  regulation.  The  best 
method  for  arriving  at  a  decision  is  to  figure  the  necessary 
mass  X  radius  squared,  from  equation  (8)  of  paragraph  5, 
Chapter  IX,  great  care  being  taken  really  to  include  in  the 
equation  every  bit  of  the  energy  beyond  control  of  the  governor. 
If  the  latter  energy  is  very  small,  the  problem  can  be  solved  by 
the  use  of  a  very  prompt  governor  (Chapter  IV,  paragraph  2 
of  Chapter  IX),  except  in  the  case  of  hydraulic  turbines  with 
long  pipe  lines. 

Third,  the  oil  pot  is  adjusted  too  tight.  This  can  readily  be 
investigated  by  changing  the  adjustment  of  the  gag  pot.  The 
remedy  is  obvious,  but  loosening  the  oil  pot  may  bring  never- 
ending  vibrations  (paragraph  2  of  Chapter  IX),  in  which  case  the 
trouble  is  traced  back  to  the  cases  of  either  insufficient  flywheel, 
or  too  small  static  fluctuation,  or  too  great  a  traversing  time. 


202    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

Fourth,  the  traversing  time  of  the  governor  is  too  great 
(governor  is  not  prompt  enough).  This  condition  is,  likewise, 
best  detected  by  calculation.  The  governor  must  be  replaced 
by  a  higher  grade  governor  (Chapter  IV)  with  high  rotative 
speed,  large  orbit  of  weights  and  spring  loading. 

Fifth,  the  governor  is  too  small  and  takes  too  much  time 
to  move  the  power-control  mechanism  to  its  new  position. 
Insufficient  size  or  capacity  of  the  governor  has  either  one  or 
both  of  two  effects.  First,  the  governor  cannot  overcome  the 
frictional  resistance  of  the  power-control  mechanism  (para- 
graph 5  of  Chapter  II),  and  second,  the  governor  cannot  move 
the  mass  of  that  mechanism  fast  enough  (Chapter  IV).  In 
either  case  the  governor  must  be  replaced  by  a  larger  one,  or 
else  the  resisting  force  and  mass  must  be  reduced  or  a  relay 
governor  must  be  installed. 

Sixth,  the  static  fluctuation  is  too  small.  This  reduces  the 
period  of  vibration  and  either  requires  much  damping,  or  else 
causes  never-ending  speed  fluctuations,  unless  tangential  inertia 
is  used.  See  paragraph  2  of  Chapter  IX.  Static  fluctuation 
can  be  measured  by  the  following  method  :  Operate  the  engine 
or  turbine  with  absolutely  constant  load  conditions  at  no  load, 
50  %  of  maximum  load  and  95  %  to  98  %  of  maximum  load  (the 
latter  should  be  100  %,  but  it  is  better  to  stay  below  the  maxi- 
mum to  avoid  getting  beyond  the  range  of  the  governor),  with 
the  oil  gag  pot  set  so  tight  that  all  vibrations  are  eliminated. 
Measure  the  speeds  and  determine  from  them  the  static  fluc- 
tuation (paragraph  1  of  Chapter  III).  From  equation  (5), 
paragraph  2  of  Chapter  IX,  find  whether  this  value  is  too  small 
or  not.  The  static  fluctuation  must  be  increased,  either  perma- 
nently by  a  change  in  the  governor,  or  temporarily  by  a  com- 
pensating oil  pot  (paragraph  2  of  Chapter  IX,  and  paragraph  2 
of  Chapter  XIII). 

4.  The  Governor  Vibrates —  (Jerks,  Dances).  —  In  engines, 
the  flywheel  may  be  too  light  so  that  cyclical  speed  fluctu- 
ation keeps  the  governor  alive,  but  in  the  great  majority 
of  cases  the  governor  is  too  light  for  the  vibratory  forces  im- 
pressed upon  it  by  the  valve  gear.  The  valve  gear  can,  in  a 
few  cases,  be  so  altered  that  the  reacting  force  is  kept  away 


GOVERNOR    TROUBLES    AND    THEIR    REMEDIES  203 

from  the  governor.  In  the  majority  of  cases  the  resistibility 
(Chapter  VIII)  must  be  increased.  This  is  done  by  adding  a 
friction  brake,  or  by  making  the  gag  pot  more  effective.  If 
either  one  of  these  two  remedies  results  in  too  great  a  speed 
variation  with  sudden  changes  of  load,  a  heavier  and  more 
massive  governor  is  needed. 

5.  Joints  or  Knife  Edges  in  the  Governor  Wear  too  Fast. 
-  The  trouble  is  due  to  one  of  two  causes  :    Either  the  gov- 
ernor is  too  small,  or  it  is  not  adapted  to  the  type  of  valve  gear 
which  it  has  to  handle.    Knife  edges  and  joints  with  small  diam- 
eter pins  are  very  good  in  governors  which  are  subjected  either  to 
no  shaking  (vibratory)  forces,  or  to  vibratory  forces  which  are 
so  small  in  comparison  to  the  size  of  the  governor  that  very 
little,  if  any,  cyclical  vibration  results.    Particularly  obj ectionable 
are  knife  edges  which  are  vibrated  while  heavily  loaded. 

The  trouble  can  be  remedied  in  several  ways.  A  new 
governor  may  be  installed  transmitting  forces  directly  from 
centrifugal  weights  to  spring,  without  joints.  Or  a  larger 
governor  may  be  installed  so  that  the  vibratory  force  becomes 
small  in  comparison  with  the  size  of  the  knife  edges,  or  else 
the  governor  may  be  redesigned  and  may  be  provided  with 
large  pins  with  light  unit  pressure.  Friction  is  not  harmful 
in  such  a  case,  because  the  vibratory  force  eliminates  it  (para- 
graph 4  of  Chapter  IX)  as  long  as  the  impressed  force  is  great 
enough  to  maintain  cyclical  vibration. 

6.  Machine  Design  Troubles.  —  Governors  are  subject  to 
a  number  of  troubles  which  are   in  no   manner  attributable 
to  their  governor-features,  but  are  solely  machine  design  or 
workmanship  difficulties.    Among  them  are  :  heating  and  wear 
of  collar  in  spindle  governors  ;    wobbling  of  governor  due  to 
unbalanced  centrifugal  masses  ;  buckling  of  compression  springs; 
stripping  of  governor  gears  due  to  non-uniform  rotational  speed 
of  driving  shaft ;  wear  of  clutches  in  mechanical  relay  governors  ; 
vibration  of  water  pipes  in  hydraulic  governors  due  to  water 
hammer  ;   and  many  more. 

These  difficulties  are  so  bound  up  with  general  machine 
design  and  shop  practice  that  their  discussion  would  by  far 
exceed  the  limits  of  the  present  volume. 


CHAPTER  XV 


THE  SELF-REGULATING  FEATURES  OF  PRIME   MOVERS  AND 
OF   MACHINERY  OPERATED   BY  THEM 

IN  Chapter  I  mention  was  made  of  the  superfluity  of 
governors  under  certain  working  conditions  of  engines  or 
turbines.  If,  for  instance,  the  resisting  torque  grows  either 
directly  with  the  speed,  line  (jf)  (2)  of  Fig.  132,  or  with  a  higher 
power  of  the  speed,  curve  (1)  (3),  and  if  the  torque  is  not 

subject  to  any  variables  indepen- 
dent of  the  speed,  then  a  gover- 
nor is  rather  superfluous,  because 
the  combination  of  prime  mover 
and  resistance  is  perfectly  self- 
governing. 

Cases  of  this  description  need 
not  be  considered  here  ;   but  even 
where  governors  are  needed,  simi- 
lar self-regulating  features  are  fre- 
quently met  with.     We  will  nov/ 
investigate  to   what  extent   such 
features  may  be  depended  upon  to  assist  close  governing. 
The  problem  comprises  two  subdivisions,  namely  : 

(1)  the  self-regulating  features  of  prime  movers  proper, 

(2)  the  self-regulating  features  of  their  load. 

In  studying  the  prime  mover  proper,  we  recognize  that 
friction  of  the  working  fluid  furnishes  the  principal  means  of 
self-regulation.  In  a  steam  engine,  the  average  torque  per 
revolution,  for  a  given  position  of  the  power-control  mechanism, 
may  be  expressed  by  the  formula  M  =  M0  —  ku2,  where  M0 
is  the  torque  which  would  be  obtained  if  the  working  fluid  were 
devoid  of  friction,  and  where  k  expresses  frictional  resistance 
per  unit  of  angular  velocity,  k  depends  upon  the  relative  size 

204 


Angularvelocity 
FIG.  132 


SELF-REGULATING  FEATURES  OF  PRIME  MOVERS          205 

of  the  steam  pipe,  its  length  from  the  boiler  to  the  engine,  the 
size  of  the  steam  and  exhaust  ports,  conditions  of  exhaust 
pipe,  capacity  of  condenser,  etc.  In  engines  with  throttle 
control,  k  is  very  much  greater  than  in  engines  with  cut-off 
control. 

A  quantitative  estimate  of  the  regulating  properties  of 
throttling  may  be  gained  from  the  following  simple  calculation  : 
The  influence  of  the  throttle  is  greatest  if  the  down-stream 
pressure  (throttle  pressure)  is  less  than  53%  of  the  up-stream 
pressure.  In  that  case  the  weight  flowing  is  proportional  to 
the  product  of  initial  steam  pressure  multiplied  by  throttle 
area.  As  long  as  these  two  quantities  are  constant,  —  and 
they  are  constant  for  a  given  position  of  the  power-control 
mechanism  —  the  rate  of  flow  remains  constant.  But  tha 
weight  flowing  in  unit  time  is  proportional  to  cylinder  displace- 
ment in  unit  time  multiplied  by  density  of  steam  after  passing 
the  throttle,  and  the  density  is  roughly  proportional  to  the  mean 
effective  pressure.  Also,  we  have  the  relation  that  cylinder 
displacement  in  unit  time  is  proportional  to  angular  velocity. 
Taking  all  these  facts  together,  we  find  that  roughly  m.e.p.  X  u 
=  constant,  or  in  words,  mean  effective  pressure  times  angular 
velocity  is  constant.  Let,  for  instance,  the  angular  velocity 
grow  by  one  per  cent,  then  the  mean  effective  pressure,  and 
with  it  the  torque,  drops  one  per  cent.  And  vice  versa,  if 
the  torque  drops  one  per  cent,  the  speed  grows  one  per  cent. 

Now  compare  this  to  regulation  by  a  governor.  If  the  speed 
grows  one  per  cent,  the  torque  drops  from  25%  to  50%,  de- 
pending upon  the  design  of  the  governor.  It  is  evident  that  the 
self-regulating  properties  of  steam  engines  cannot  be  counted 
upon  whenever  close  regulation  is  essential. 

It  must  be  admitted  that  in  a  few  exceptional  cases  the 
influence  of  throttling  is  greater  than  that  which  is  apparent 
from  the  above  calculation,  particularly  in  noncondensing 
engines  with  expansion  below  the  back  pressure.  But  these 
exceptions  are  so  few  that  their  scarcity  confirms  the  rule. 

A  study  of  the  self-regulating  properties  of  steam  turbines 
and  hydraulic  turbines  yields  exactly  the  same  result  which  was 
found  from  the  above  simple  calculation  (namely  that  for 


206    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 


one  per  cent  growth  of  speed,  the  torque  drops  one  per  cent) 
although  the  mechanics  of  self-regulation  of  turbines  is  very 
different  from  that  of  the  corresponding  property  of  engines. 
From  the  theory  of  turbines  it  is  known  that,  for  a  given  throttle 
opening,  the  torque  M  exerted  at  angular  velocity  u  is  given 
by  the  equation 


where  M  0  is  the  torque  developed  at  speed  u0,  and  where  both 
Mo  and  u0  refer  to  the  "best"  speed  of  the  turbine,  that  is  to 
say,  to  the  speed  at  which  it  develops  its  greatest  power.  By 

M0  dM          du 

differentiation  we  obtain  dM  =  —  —  du  :  or  -77-  =  —  —  which. 

U0  MO  U0 

in  plain  English,  means  that  for  one  per  cent  drop  of  angular 
velocity,  the  torque  grows  one  per  cent.  We  can,  therefore, 
only  repeat  the  statement  that  the  self-regulating  tendencies 
cannot  and  must  not  be  depended  upon  for  close  regulation. 

In  internal  combustion   engines   conditions   are  even  less 
favorable  to  self-regulation.    While  throttling  of  gases  through 

the  ports  exerts  influence 
similar  to  that  described  be- 
fore under  steam  engines, 
the  effect  of  ignition  may  be 
either  favorable  or  un- 
favorable to  the  point  under 
discussion,  as  will  presently 
be  understood.  In  Fig.  133 
let  (i)  be  a  normal  indicator 
card.  If  the  ignition  be  ad- 
vanced (so  that  the  spark 
occurs  earlier),  card,  (2)  will 
result.  If  the  spark,  on  the 
contrary,  be  retarded,  card  (8)  will  be  obtained.  If  an  engine 
operates  with  a  very  early  spark,  even  a  slight  slowing  down 
will  cause  the  combustion  to  be  completed  in  a  smaller  frac- 
tion of  the  stroke  of  the  engine  ;  a  condition  of  premature 
ignition  is  approached,  the  area  of  the  indicator  card  (the 
work  per  stroke)  falls  off,  the  engine  slows  down  still  more, 


FIG.  133 


SELF-REGULATING  FEATURES  OF  PRIME  MOVERS          207 

and  so  forth  with  cumulative  effect.  In  that  case  the  engine 
has  absolutely  no  self-regulating  features ;  it  is  positively 
unstable,  and  may  even  thwart  the  influence  of  the  governor, 
unless  the  latter  be  very  quick  in  its  action.  In  the  opposite 
case  of  a  late  spark  there  is  greater  stability,  but  the  fuel  con- 
sumption is  so  high  as  to  preclude  the  operation  of  engines 
with  that  adjustment,  except  very  occasionally  under  excep- 
tional circumstances. 

Summarizing,  we  find  that  the  self-regulating  features  of 
prime  movers  cannot  be  depended  upon  as  a  help  to  close 
regulation,  but  that  they  are  of  assistance,  if  crude  or  coarse 
regulation  only  is  aimed  at. 

We  find  a  very  similar  situation  if  we  investigate  the  second 
part  of  the  problem,  namely  the  governing  influence  of  the  load 
or  resistance  against  which  the  prime  mover  works.  No  matter 
whether  a  prime  mover  drives  machinery  directly,  or  whether 
it  does  so  by  means  of  electrical  transmission  of  power,  there 
is  almost  invariably  an  increase  of  torque  required  if  the  speed 
grows.  This  condition 
is  frequently  due  to  in- 
creased air  resistance, 
and  frequently  to  other 
causes.  Consider,  for 
example,  an  electric 
lighting  system,  a  dia-  FlG-  134 

gram  of  which  is  shown  in  Fig.  134.  (1)  is  the  generator,  and 
(2}  are  the  lights.  Unless  counteracted  by  a  voltage  regulator, 
an  increase  of  speed  produces  a  corresponding  increase  of 
electromotive  force,  and  the  latter  results  in  a  proportional 
increase  of  current.  Hence,  a  one  per  cent  growth  of  speed 
produces  2  %  increase  in  power  ;  but,  since  power  is  speed  times 
torque,  the  2  %  increase  of  power  is  evenly  divided  between  the 
assumed  1  %  rise  of  speed  and  the  necessarily  resulting  1  %  in- 
crease of  torque. 

It  should  be  noted  that  this  increase  of  resisting  torque 
occurs  only  on  condition  that  the  external  resistance  of  the 
circuit  remains  constant.  Switching  lights  on  and  off,  of  course, 
varies  the  torque  independently. 


208    GOVERNORS  AND  THE   GOVERNING  OF  PRIME   MOVERS 

In  practice,  very  few  cases  with  independently  variable 
external  resistance  are  encountered  in  which  for  a  given  con- 
dition of  such  resistance  (whether  electrical,  hydraulic  or  me- 
chanical) the  resisting  torque  grows  faster  than  the  square  of 
the  speed,  which  means  that  for  one  per  cent  increase  of  speed 
the  resisting  torque  practically  never  grows  more  than  two 
per  cent. 

Couple  with  this  result  the  conclusion  reached  before, 
namely  that  for  one  per  cent  increase  of  speed  the  driving 
torque  never  drops  more  than  one  per  cent,  and  we  have  the 
final  conclusion  that  one  per  cent  growth  of  speed  never  pro- 
duces self-regulating  features  amounting  to  more  than  three 
per  cent  of  the  existing  torque.  This  conclusion  allows  nothing 
but  a  reiteration  of  the  statement  previously  made,  that  the 
self-regulating  properties  of  prime  movers  and  of  their  loads 
cannot  be  counted  upon,  if  close  regulation  is  desired,  but  that 
they  are  of  considerable  assistance  if  coarse  regulation  is 
permissible. 

Reference  to  Bibliography  at  end  of  book:  28. 


Xi: 


APPENDIX 

ELEMENTARY  DERIVATION  OF  EQUATION   (3)   OF 
PARAGRAPH  1,  CHAPTER  II 

Let  C  be  the  centrifugal  force  caused  by  angular  velocity  u,  mass  m, 
and  by  radius  r,  and  let  Ci  be  the  centrifugal  force  caused  by  angular 
velocity  u1  ';  m  and  r  remaining  the  same  as  before;  then 

C   =  mru? 
d=mr  (u'Y 


Ci-C  =  mr  (u'2  -uz)  =mr  (uf  -  u)  (uf  +  u) 

2(V  -  u) 


\  -  C  =  m  r 


u) 


u'  +  u 

but  — - —  =  ua  =  average  between  u'  and  u, 

&  ii 

hence  (7,  -  C  -  O,^-^, 

Wa 

where  Ca  =  average  value  of  centrifugal  force. 

Let    Ci-C  =  DC,        and      ui  -  u  =  Du, 

then  DC  =  —  Ca] 

Ua 

but  for  small  changes  of  u,  Ca  and  ua  differ  very  little  from  C  and  w, 
so  'that  approximately 


U 

DETENTION  BY  FRICTION 

The  detention  which  will  be  calculated  is  that  of  friction  due  to 
centrifugal  forces  and  weight  or  spring  forces;  but  it  does  not  include 
that  friction  due  to  compound  centrifugal  forces  (Coriolis*  force).  It 
is,  therefore,  only  correct  for  slow  changes  of  position  of  the  governor. 

The  force  acting  on  a  pin  causes  a  moment,  due  to  friction,  which 
may  be  expressed  thus: 

af-Qi/r, 

209 


210    GOVERNORS  AND  THE   GOVERNING   OF   PRIME   MOVERS 


where  Qi  is  the  force  on  the  pin  bearing,  /  is  the  coefficient  of  friction, 

and  r  is  the  pin  radius. 

In  any  particular  linkage,  for  instance  that  shown  in  Fig.  135,  the 

moments  produced  by  friction  on  the  pins  (1)  and  (2)  may  be  combined 

into  the  moment  of  a  single  force,  as 
Q,  in  any  direction,  having  a  moment 
arm  L,  which  is  the  perpendicular 
dropped  from  (3),  the  instantaneous 
center  of  rotation  of  the  two  pins. 


FIG.  135 


The  force  Q  may  have  its  point  of 
application  transferred  along  its  line 
of  action,  and  may  then  be  combined 
with  other  forces,  until  all  are  com- 
bined into  a  single  force. 


In  the  Watt  type  of  governor,  shown  in  Fig.  136,  for  pins  (1)  and  (2) 


taking  Qa,  in  this  case,  in  the  line  of  direction  of  the  next  link,  to  which 

(1)  (2)  is  connected. 

Qa  is  the  force  in  the  direction  (2)  (3). 

Ml       Oin 


Qr   =  Qa  COS  I 

Qr  is  a  force  acting  through  (3)}  vertically. 

_  ,  Qi  ri  +  Qz  r2  _    Qz  r2  +  Qi 

r  J  f       I  .  J 


f       I  .  7 

La/cos  i  LI 

For  pins  (2)  and  (3),  Qb  L2  =  M2  =  f  Q2  r2  +  /  Q3  r3 

M 


L, 


Qb  is  also  a  vertical  force  through  (3). 
Combining  the  two  forces  Qr  and  Qb, 


, 

LI 


APPENDIX  211 

and  since  in  this  case  all  of  the  pins  have  the  same  diameter, 
F          fQ,  +  Q2 


2 


In  the  governor  shown  in  Fig.  136,  when  in  mid-position, 

L2  =  13i"  r  =  .25" 

Zi  =  17"  Assume    /  =  .10 

The  forces  may  be  found  graphically,  as  shown  in  Fig.  137. 

The  total  centrifugal  force,  C,  of  one  weight  is  considered  as  divided 


cq  -  — 


FIG.  136 


FIG.  137 


into  two  parts,  one  of  which,  Cw,  holds  the  fly-weight  in  equilibrium 
while  the  other,  Cq,  holds  the  counterpoise  in  equilibrium.  Since 
neither  Cw  nor  W  acts  on  pin  (2),  their  resultant  acting  on  (1)  must 
lie  in  the  direction  (1)(4)  (Fig.  137);  and  by  drawing  the  force  triangle 
at  (1),  one  of  the  forces,  Zi,  acting  on  pin  (1)  is  found. 

The  weight  Q  (J  weight  of  counterpoise)  is  held  in  equilibrium  by 
two  forces,  one  of  which  (horizontal)  is  balanced  by  the  corresponding 
force  from  the  other  side  acting  through  the  collar.  The  other  com- 


212    GOVERNORS  AND   THE   GOVERNING   OF   PRIME   MOVERS 

ponent  Z2  acts  in  the  direction  of  the  link  (2)  (8),  and  as  this  is  regarded 
as  a  massless  rod,  it  is  the  only  force  acting  on  (2)  and  (3),  hence 


The  direction  of  the  force  (Z3)  on  (1)  produced  by  Z2  and  CQ  is 
found  from  the  consideration  that  all  forces  on  a  link  must  (for  equi- 
librium) pass  through  a  common  point,  which  in  this  case  is  (m).  The 
magnitude  of  the  force  Z3  is  found  by  drawing  the  triangle  of  forces, 
shown  above  (1)  in  the  figure. 

The  total  force  acting  on  (1)  is  the  resultant  of  Z\  and  Z3,  or  force 
(6)(e),  Fig.  137. 

Force  (b)  (e)  =  Qi 

W  =  16  pounds  Q   =  59  pounds, 

and  for  mid-position,  Qi  =  90  Q2  =  Q3  =  84. 

-  =  .25  X  .10  X  (-  -  +  -  -  }  =  .573,  friction  in  one  half. 
2  \  17       13j/ 

Total  friction,  both  sides  of  governor  =  F  =  1.146  pounds. 
Strength  of  governor  =  140  pounds  =  P. 


The  detention  due  to  governor  friction  in  the  particular  Watt-type 
governor  shown  in  Fig.  56  is  — 

j_/rf2Li=4 


I  L2 

L2  =  161*.  r    =  .25" 

I     =  201*.  /    =  -10 

Qi  =  315.  Q2  =  Q3  =  193. 


F  =  2.442 

F      2.442 


In  the  Hartung  governor,  shown  in  Fig.  28,  no  centrifugal  forces 
are  transmitted  to  the  pins,  except  that  necessary  to  balance  the  weight 
of  the  collar  =  40  pounds 


APPENDIX  213 


? 


PI  =  strength  of  governor  =  1100  pounds 
r  =  radius  of  pins  =  .25 " 
=  lever  arm  (1)  (2)  =  5." 
=  lever  arm  (2)  (3)  =  5.71" 


Weight  of  one  fly-weight  =  79  pounds. 


Figure  for  mid-position : 

Horizontal   force    on    (1)    to    counterbalance   J    of   collar   weight 

—  =  22.84  pounds.      This  force  also  acts  on  (2),  in  opposite 
5 

direction. 


Pin  (1) Qi  =  V(22.84)2  +  (79)2  =  82.1. 

If  the  collar  moves  a  small  distance  Ds,  then  the  rubbing  path  of  fric- 

5      .25 

tion  force  on  pin  (1)  is  Ds  •  — — •  •  —  =  .0437  Ds. 

o.71      o 

Assume  friction  coefficient  =  .10 

Friction  work  on  (1)  =  .10  x  82.1  x  .0437  Ds  =  .3595  Ds. 


Pin  (2) Q2  =  V(22.84)2  +  (79  +  20)2  =  101.9. 

.25 

Rubbing  path  =  Ds  -L— 
5.71 

Friction  work  =  .10  X  101.9  x  .0437  Ds  =  .446  Ds. 

Pin  (3) Q3  =  20. 

Friction  work  =  .10  x  20  X  0.437  Ds  =  .0874  Ds. 

Pin  (4) Q4  =  20. 

In  mid-position,  rubbing  path  =  0,  Friction  work  =  0. 

Total  friction  work  =  (.4460  +  .3595  +  .0874  +  0)  Ds  =  .8929  Ds. 

F      .8929  Ds 

Equivalent  force  at  collar,  —  =  — — =  .8929 

2  Ds 

F  =  1.7858  pounds. 

F      1  7858 
q  =  —  =  -  — —  =  .001623  for  mid-position. 

sr         llUl) 


214    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

CENTRIFUGAL  MOMENT   OF   OBLONG   WEIGHTS 

M  =  Centrifugal  Moment  = 
fdm  u2(r  +  x)  (y  +  L)  =  fdm  u2ry 
+  f  dm  u2  rL  +  fdm  u2xy  +  fdm  u2 
X  L  but  fdm  y  =  0  and  fdm  x 
=  0,  because  (2)  is  mass  center. 
fdm  u2rL  =  mu2rL.  See  Fig.  140. 

To  find  a  simpler  expression  for 
fdm  x  y,  refer  it  to  the  principal 
axes  X'Y',  and  call  the  coordinates 
x',  y'.  For  these  axes  fdm  x'y'  =  0, 
because  the  moments  of  inertia  are 
a  maximum  and  a  minimum.  By 
analytical  geometry:  x  =  xf  cos  k  + 
y'  sin  k,  and  y  =  —  x'  sin  k  +  y'  cos  k. 
Substitute  in  fdm  x  y  and  carry  out 
multiplication 

fdm  x  y  =  —  fdm  x'2  sin  k  cos  fc  +  f  d  m  y'2  sin  k  cos  fc. 

The  two  terms  containing  the  product  x'y1  vanish,  as  above  explained. 

Substitute  In!  dA  m'  for  dm,  where  h'  =  thickness  at  right  angles  to 

paper,  dA  =  differential  of  area  in  plane  of  paper,  m'  =  mass  per  unit 

volume.    Then 

fdm  x'2  sin  k  cos  k  =  In!  m'  \  sin  2  k  J(y')  and 

fdm  y'2  sin  k  cos  k  =  h'  m'  J  sin  2  k  J(x'), 

where  J(x')  means  the  moment  of  inertia  of  the  plane  section  of  the 
centrifugal  weight  about  the  X'  axis,  and  J(y')  the  corresponding  mo- 
ment about  the  Y'  axis. 

With  these  notations  the  centrifugal  moment  is 

M  =  m  r  u2  L  +  J  h'  m'  u2  sin  2  k  (J(X>)  -  J(y>)} 

In  the  text  Jiong  and  J short  were  used  in  place  of  Jx>  and  Jy>.  This  is 
correct  for  the  illustration,  but  must  be  replaced  by  J8  —  Ji,  if  the  X' 
direction  is  longer  than  the  F'  axis. 


FIG.  140 


DETAIL  CONSTRUCTION  OF  CHARACTERISTIC 
FOR  FIGURE  31 

In  the  illustration  (Fig.  138),  (1),  (2),  (3),  (4),  (5)  are  different 
positions  of  the  mass  center  of  the  centrifugal  weight;    (11), 


APPENDIX 


215 


CqforincreasedQ. 


FIG.  138 


(13),  (14),  (15)  are  the  corresponding  positions  of  the  inner  end  of  the 
bell  crank;  (21)  (22),  (23),  (24),  (25)  are  the  corresponding  positions 
of  the  upper  end  of  the  connecting  link;  point  (16)  is  the  intersection  of 
the  horizontal  through  (1)  and  the  straight  line  (11)  (21)',  points  (17), 


216    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

(18),  (19),  (20)  are  found  by  intersection  of  corresponding  lines  for  the 
other  positions.  The  values  of  W  =  15  pounds,  Q  =  45  pounds  and 
increased  Q  =  45  +  85  pounds  have  been  laid  off  near  point  (10), 
(right-hand  bottom  Fig.  138)  to  the  scale  of  one  inch  representing  100 
pounds.  The  triangle  of  forces  which  is  shown  in  Fig.  32  has  been 
reproduced  in  convenient  form  for  construction  on  Fig.  138,  as  shown  in 
this  sketch.  The  same  construction  has  been  carried  out  with  increased 
Q,  and  with  the  various  spring  forces,  each  spring  force  being  computed 
from  the  "  initial  tension  plus  scale  times  deflection."  The  spring  force 
for  position  (2)  has  been  marked. 

The  centrifugal  forces  necessary  to  balance  the  weight  of  the  cen- 
trifugal masses  are  found  by  a  series  of  triangles  of  forces  below  point 
(10).  The  various  centrifugal  forces  have  been  laid  off  and  combined 
above  the  respective  positions  of  the  centrifugal  mass.  For  position  (3), 


Angular  velocity  =  J32'2  x  12  y^  =  2.09  Vc 
x  15  X  5.9 


APPENDIX 


217 


Ordinate  represents 
Cross-sectioned  area. 


Or  d  incite  represents 
Cross/Sectioned  area 


Method  of  Finding  Angular 
Displacement—from  Impressed  Moment. 

FIG.  139 


The  illustration,  Fig.  139,  shows  a  method  of  finding  angular  dis- 
placement from  a  curve  of  impressed  moments,  as  exemplified  by  the 
moment  caused  by  gravity.  The  illustration  is  so  clear  that  it  needs 
no  comment,  with  the  exception  that  the  units  and  scales  must  be 
carefully  watched. 


BIBLIOGRAPHY 

The  following  is  offered  not  as  a  complete  and  comprehensive 
bibliography,  but  as  a  list  of  the  most  important  and  most  readily 
accessible  contributions  to  governor  science.  While  some  of  the 
articles  referred  to  contain  theories  and  statements  of  doubtful  value, 
they  have  been  included  for  the  purpose  of  illustrating  the  historical 
development  of  the  theory  of  governing. 

1.  ANGUS,  R.  W.    Theory  of  Machines,  part  I,  Principles  of  Mechan- 

ism; part  II,  Elementary  Mechanics  of  Machines.  Ed.  2.  340 
pages.  1917.  McGraw. 

Chapter  XII,  pp.  201-239,  treats  of  "  Governors";  Chapter 
XIII,  pp.  240-260,  treats  of  "  Speed  Fluctuation  in  Machinery." 
Considerable  Mathematics  involved. 

2.  ARMSTRONG,  E.  J.     Use  for  Inertia  in  Shaft  Governors.     1890. 

(In  Transactions  of  the  American  Society  of  Mechanical  En- 
gineers, vol.  11,  pp.  1068-1070.  Discussion,  pp.  1070-1080.) 
Non-mathematical  treatment  of  the  function  of  inertia  in  shaft- 
governor  design. 

3.  ARMSTRONG,  E.  J.    New  Shaft  Governor.    1895.    (In  Transactions 

of  the  American  Society  of  Mechanical  Engineers,  vol.  16, 
pp.  729-733.  Discussion,  pp.  733-738.) 

Description  of  construction  and  operation  of  a  governor  em- 
ploying a  shifting  weight,  the  operation  of  which  is  said  to  be 
practically  isochronous. 

4.  Automatic   Electric   Regulator  for  Steam   Engines.     1903.     (In 

Western  Electrician,  vol.  33,  pp.  480-481.) 

Devoted  mainly  to  an  illustrated  description  of  the  method 
of  operation. 

6.  BALL,  F.  H.  Improved  Form  of  Shaft  Governor.  1888.  (In 
Transactions  of  the  American  Society  of  Mechanical  Engineers, 
vol.  9,  pp.  300-309.  Discussion,  pp.  309-323.) 

Illustrated  description  of  several  different  shaft  governors, 
with  special  attention  to  a  dashpot  scheme  devised  by  the 

author. 

219 


220    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

6.  BALL,  F.  H.    Steam  Engine  Governors.     1897.     (In  Transactions 

of  the  American  Society  of  Mechanical  Engineers,  vol.  18, 
pp.  290-308.  Discussion,  pp.  308-313.) 

Goes  into  the  history  of  the  development  of  governors  in 
""general,  and  draws  conclusions  as  to  the  relative  importance  of 
the  several  governing  forces.     ~7J7' 

7.  BEGTRUP,  J.     Theory  of  Steam  Engine  Governors.     1893-1894. 

(In  American  Machinist,  vol.  16,  Oct.  19,  1893,  pp.  2-3;  vol.  16, 
Dec.  14,  1893,  pp.  2-3;  vol.  17,  Jan.  18,  1894,  pp.  1-3;  Mar.  1, 
1894,  pp.  1-3;    May  3,  1894,  pp.  2-3.)     /  J  ± 
Not  excessively  mathematical  in  treatment. 

8.  BUDAU,  A.     Die  Geschwindigkeitsregulierung  der  Turbinen  vom 

Ende  der  achtziger  Jahre  des  vorigen  Jahrhunderts  bis  auf  den 
heutigen  Tag.      1905.      (In    Zeitschrift   des   Oesterreichischen 
Ingenieur-  und  Architekten-Vereines,  vol.  57,  pt.  2,  pp.  621-631.) 
Construction  and  theory  of  operation  of  governors. 

9.  BUDAU,  A.     Ueber  die  Americanischen  Turbinenregulatoren  mit 

besonderer  Beriicksichtigung  des  Lombard-  und  Sturgess-regu- 
lators.  1908.  (In  Elektrotechnik  und  Maschinenbau,  vol.  26, 
pp.  8-12,  28-33.) 

Theoretical  treatment. 

10.  BUVINGER,  G.  A.  Turbine  Design  as  Modified  for  Close  Regula- 
tion. 1906.  (In  Transactions  of  the  American  Society  of  Me- 
chanical Engineers,  vol.  27,  pp.  698-710.) 

Concerned  principally  with  design  of  gates,  but  includes  con- 
sideration of  flywheel  effect  of  generator  and  turbine,  effect  of 
draft  tube  and  character  of  load. 

CHARNOCK,  G.  F.  Governors  and  the  Speed  Regulation  of  Steam 
Engines.  1908.  (In  Mechanical  Engineer,  vol.  22,  pp.  674-677, 
687-690,  738-740,  754-756.) 

Chiefly  theoretical  in  treatment.       U 

12.  CHURCH,  I.  P.     Governing  of  Impulse  Wheels.     1905.     (In  En- 

gineering Record,  vol.  51,  p.  214-215.) 

Concerned  with  hydraulic  conditions  produced  in  a  water 
wheel  supply  pipe  when  the  governor  is  in  action. 

13.  COLLINS,  H.  E.    Shaft  Governors,  Centrifugal  and  Inertia;  Simple 

Methods  for  the  Adjustment  of  all  Classes  of  Shaft  Governors. 
127  pages.    1908.    Hill.     (Power  Handbooks.) 
Compiled  from  "  Power." 

14.  DALBY,  W.  E.     Steam  Power.     1915.     Arnold. 

Theory  of  governors  treated,  pp.  368-404. 


BIBLIOGRAPHY  221 

15.  DELAPORTE.     Determination   de   certains   elements   des   moteurs 

a  vapeur  en  vue  de  la  regulation.  1900.  (In  Revue  de  Me- 
canique,  vol.  7,  pp.  691-697.) 

Mathematical  considerations  of  conditions  of  stability  of 
regulation. 

16.  EHRLICH,  P.  Der  Einfluss  des  Tachometers  auf  den  Reguliervorgang 

indirekt    wirkender    Regulatoren.     1907.      (In    Elektrotechnik 
und  Maschinenbau,  vol.  25,  pp.  25-30,  53-56,  76-82.) 
Theoretical  treatment. 

17.  EHRLICH,  P.     Die  elastische  Verbindung  der  rotierenden  Massen 

und  ihr  Einfluss  auf  den  Reguliervorgang  des  Motors.     1906. 
(In  Zeitschrift  des  Oesterreichischen  Ingenieur-  und  Architekten- 
Vereines,  vol.  58,  pp.  152-157.) 
Theoretical  treatment. 

18.  Encyklopadie  der  mathematischen  Wissenschaften  mit  Einschluss 

ihrer  Anwendungen.     6  vols.     1904-1915.     Teubner,  Leipzig. 

"Regulierung  des  Maschinenganges "  treated  in  theoretical 
manner  by  R.  von  Mises,  vol.  4,  pt.  2,  pp.  254-296. 

19.  GARRATT,  A.  V.    Elements  of  Design  Favorable  to  Speed  Regu- 

lation in  Plants  Driven  by  Water  Power.  1899.  (In  Transac- 
tions of  the  American  Institute  of  Electrical  Engineers,  vol.  16, 
pp.  361-394.  Discussion,  pp.  394-405.) 

Describes  those  peculiarities  of  design  of  plant  which  have 
special  bearing  on  speed  regulation.  Does  not  discuss  theory  or 
construction  of  the  governor  itself. 

20.  GARRATT,  A.  V.    Speed  Regulation  of  Water  Turbines.    1914.    (In 

General  Electric  Review,  vol.  17,  pp.  557-566.) 

Discusses  speed  regulation  formulas  and  the  various  factors  en- 
tering into  them.  Treatment  theoretical  to  only  a  small  degree. 

21.  GENSECKE,  W.    Untersuchung  einer  mittelbaren  Dampfmaschinen- 

regler.      1907.      (In    Zeitschrift    des    Vereines    Deutscher    In- 
genieure,  vol.  51,  pt.  2,  pp.  1819-1824,  1895-1901.) 
Theoretical  treatment. 

22.  Gray  Electro-mechanical   Governor.      1903.      (In  Western   Elec- 

trician, vol.  32,  p.  129.) 

Devoted  mainly  to  an  illustrated  description  of  the  method  of 
operation. 

23.  GUTERMUTH,  M.  F.    Ueber  Kraftmaschinenregelung.     1914.     (In 

Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  58,  pt.   1, 
pp.  408-414,  441-447,  497-501.) 
Theoretical  treatment  and  tests  on  resistibility. 


222    GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

24.  HALL,  H.  R.    Governors  and  Governing  Mechanism.     119  pages. 

1903.     Technical  Pub.  Co.,  Manchester. 

Treats  of  governors  and  valve  gears,  and  of  their  underlying 
principles.     Illustrates  many  commercial  forms. 

25.  HARTNELL,  WILSON.     On  Governing  Engines  by  Regulating  the 

Expansion.  1882.  (In  the  Proceedings  of  the  Institution  of 
Mechanical  Engineers,  vol.  33,  pp.  408-430.  Abstract  of  Dis- 
cussion, pp.  431-439.) 

Describes  two  methods  of  controlling  the  expansion  gear  by 
means  of  a  governor.    Involves  considerable  theory. 

26.  HECK,  R.  C.  H.    Steam-engine  and  Other  Steam-motors;   a  Text- 

book for  Engineering  Colleges  and  a  Treatise  for  Engineers. 
2  vols.  1907.  Van  Nostrand. 

Vol.  2,  Chapter  10,  pp.  367-437,  on  " Governors  or  Regulators" 
contains  considerable  theoretical  data. 

27.  HENRY,  G.  J.     Regulation  of  High-pressure  Water  WTieels  for 

Power-transmission  Plants.  1906.  (In  Transactions  of  the 
American  Society  of  Mechanical  Engineers,  vol.  27,  pp.  662-680. 
Discussion,  pp.  680-681.) 

Discusses  the  feasibility  of  various  governor  schemes. 

28.  ISAACHSEN,  J.    Das  Regulieren  von  Kraftmaschinen.     1899.     (In 

Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  43,  pt.  2, 
pp.  913-918.) 

Theoretical  treatment. 

29.  JOHNSON,  R.  D.    Surge  Tank  in  Water  Power  Plants;   a  Device 

for  Aid  in  Speed  Regulation  and  Pressure  Relief  in  Water  Powers 
with  Long  Pressure  Pipes  and  High  Velocities.  1908.  (In 
Transactions  of  the  American  Society  of  Mechanical  Engineers, 
vol.  30,  pp.  443-474.  Discussion,  pp.  474-501.) 

Includes  theoretical  material  on  the  effort  of  turbine  governors 
and  on  the  differential  regulator. 

30.  KAISER,  K.   Achsenregler  mit  wahrend  des  Betriebes  zu  bedienender 

Verstellung  der  Umlaufzahl.    1911.     (In  Zeitschrift  des  Vereines 
Deutscher  Ingenieure,   vol.   55,   pt.    1,   pp.   254-259,   341-345, 
507-514.) 
Theoretical  treatment. 

31.  KITSON,  F.   W.     On   the   Allen   Governor   and   Throttle   Valve 

for  Steam  Engines.  1873.  (In  Proceedings  of  the  Institution 
of  Mechanical  Engineers,  vol.  24,  pp.  47-55.  Discussion, 
pp.  55-62.) 

Illustrated  description  of  the  governor  and  of  its  operation. 


BIBLIOGRAPHY  223 

22.  KOERNER,  C.  Dynamik  direkt  und  continuirlicher  wirkender 
Regulatoren.  1899.  (In  Zeitschrift  des  Oesterreichischen  In- 
genieur-  und  Architekten-Vereines,  vol.  51,  pp.  413-417,  428- 
432,  443-447.) 

33.  KOERNER,   C.     Untersuchung   der  Beharrungsregler  an   Dampf- 

maschinen.     1901.     (In  Zeitschrift  des  Vereines  Deutscher  In- 
genieure,  vol.  45,  pt.  2,  pp.  1842-1849.) 
Theoretical  treatment. 

34.  KOOB,  A.     Das  Regulierproblem  in  vorwiegend  graphischer  Be- 

handlung.     1904.     (In  Zeitschrift  des  Vereines  Deutscher  In- 
genieure,  vol.  48,  pt.  1,  pp.  296-303,  373-379,  409-416.) 
Theoretical  treatment. 

35.  LANZA,  G.    Dynamics  of  Machinery.     246  pages.     1911.    Wiley. 

''Governors/'  Chapter  IV,   pp.    135-199;    "Deduction  of  the 
Formulae  for  Governor  Oscillations,"  Appendix  B,  pp.  232-237. 
Mainly  theoretical,  with  considerable  mathematics. 

36.  LECORNU,  L.     Les  Regulateurs  des  Machines  a  Vapeur.     1899- 

1903.  (In  Revue  de  Mecanique,  vol.  4,  pp.  333-361,  466-485; 
vol.  5,  pp.  263-285,  611-632;  vol.  6,  pp.  285-320,  661-712; 
vol.  7,  pp.  557-570;  vol.  8,  pp.  265-279;  vol.  10,  pp.  220-237, 
309-314;  vol.  11,  pp.  243-257,  468-484;  vol.  12,  pp.  309-328; 
vol.  13,  pp.  109-121.) 

Very  comprehensive.  Includes  illustrated  descriptions  of  con- 
struction and  operation  of  many  types  of  governors,  and  the 
theory  of  governing  in  general.  (See  also  Sparre,  Comte  de.) 

37.  LOEWY,  R.     La  Theorie  des  Regulateurs  a  Ressorts  Lamellaires. 

1910.     (In  Revue  de  Mecanique,  vol.  26,  pp.  409-428.) 
Mathematical  in  treatment. 

38.  LOEWY,  R.    Der  Reguliervorgang  bei  modernen  indirekt  wirkenden 

hydraulischen  Turbinenregulatoren.     1908.     (In  Elektrotechnik 
und  Maschinenbau,  vol.  26,  pp.  195-201,  220-226.) 
Theoretical  treatment. 

39.  LONGRIDGE,  M.    On  the  Moscrop  Engine  Recorder,  and  the  Knowles 

Supplementary  Governor.  1884.  (In  Proceedings  of  the  Insti- 
tution of  Mechanical  Engineers,  vol.  35,  pp.  150-159.  Discus- 
sion, pp.  160-166.) 

Part  II,  "Knowles  Supplementary  Governor,"  pp.  157-159, 
gives  brief  description  of  the  method  of  operation  of  that  instru- 
ment. 


224    GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

40.  MANSFIELD,  A.  K.     Notes  on  the  Theory  of  Shaft  Governors. 

1894.     (In  Transactions  of  the  American  Society  of  Mechanical 
Engineers,  vol.  15,  pp.  929-949.    Discussion,  pp.  949-960.) 
^^     Theoretical  treatment. 

41.  MEAD,  D.  W.    Water  Power  Engineering;  the  Theory,  Investiga- 

tion  and   Development   of  Water   Powers.     Edition   2,    1915. 
McGraw.      "  Speed   Regulation    of    Turbine    Water    Wheels," 
Chapter  14,  pp.  408-459.     " Literature/'  pp.  456-459.     "The 
Water  Wheel  Governor,"  Chapter  15,  pp.  460-501. 
Mainly  theoretical  in  treatment. 

42.  MERKL,  F.  R.  v.    Die  Tourenregulierung  von  Kraftmaschinen  mit 

Hilfe  einer  Leitgeschwindigkeit  mit  moglichster  Vermeidung  der 
periodischen  Schwankungen.  1908.  (In  Elektrotechnik  und 
Maschinenbau,  vol.  26,  pp.  763-769.) 

Comparatively  nontechnical  treatment  of  chronometric  or 
interference  governors. 

^3.   MISES,  R.  v.    Zur  Theorie  der  Regulatoren.     1908..    (In  Elektro- 
technik und  Maschinenbau,  vol.  26,  pp.  783-789.) 

Theoretical  treatment. 

44.  MOOG,  0.     Neue  Turbinenpendel  der  Regulatorenbaugesellschaft 

deTemple  in  Leipzig.  1913.  (In  Zeitschrift  fur  das  gesamte 
Turbinenwesen,  vol.  10,  pp.  161-163,  183-186,  200-202.) 

Describes  pendulum  governor  of  the  deTemple  Governor 
Construction  Co.,  Leipzig,  and  devotes  considerable  space  to 
a  consideration  of  the  theory  involved. 

45.  New  Governor  for  Water  Turbines.    1914.    (In  Engineer,  vol.  117, 

pp.  407^08.) 

Illustrated  description  of  the  Pitman  water  turbine  governor. 

46.  New  Type  of  Pelton-wheel  Governor.     1913.     (In  Engineering 

Record,  vol.  68,  pp.  186.) 

Brief  illustrated  description  of  governor,  the  main  purpose  of 
which  is  to  prevent  water-hammer  in  the  penstock,  but  at  the 
same  time  to  cut  off  the  water  from  the  wheel  immediately. 

47.  PFARR,  A.     Der  Reguliervorgang  bei  Turbinen  mit  indirekt  wir- 

kendem  Regulator.    1899.    (In  Zeitschrift  des  Vereines  Deutscher 
Ingenieure,  vol.  43,  pt.  2,  pp.  1553-1558,  1594-1599.) 
Theoretical  treatment. 

48.  PITMAN,  P.  H.     Improved  Governor  for  Water  Turbines.     1913. 

(In  Proceedings  of  the  Institution  of  Mechanical  Engineers, 
vol.  77,  parts  1-2,  pp.  565-577.) 


BIBLIOGRAPHY  225 

(The  same,  abstract,  1914.  In  Zeitschrift  fur  das  gesamte 
Turbinenwesen,  vol.  11,  pp.  519-520.) 

Describes  author's  hydraulic  relay  governor,  which  does  away 
with  floating  levers.  Nonmathematical. 

49.  PORTER,  C.  T.    Description  of  an  Improved  Centrifugal  Governor 

and  Valve.  1895.  (In  Transactions  of  the  American  Society 
of  Mechanical  Engineers,  vol.  16,  pp.  134-136.) 

Brief,  illustrated  description  of  an  improved  frictionless 
governor  so  constructed  as  to  permit  an  adjustment  which  is 
close  to  isochronous.  The  valve  used  in  connection  with  it  has 
a  balanced  stem. 

50.  PROELL,  R.    Fortschritte  im  Bau  von  Flachreglerventilsteuerungen 

nebst  einem  Beitrage  zur  Theorie  der  Fliehkraftregler.  1913. 
(In  Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  57,  pt.  2, 
pp.  1287-1295,  1339-1343.) 

Many  illustrations  of  apparatus,  but  treatment  mainly 
theoretical. 

51.  PROELL,  R.    Neuere  Flachregler  mit  regelbarer  Umlaufzahl.    1909. 

(In  Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  53,  pt.  2, 
pp.  568-572.) 

Presents  practical  application  and  theory. 

52.  RANSOM,  H.  B.    Method  of  Testing  Engine  Governors.    1893.    (In 

Minutes  of  Proceedings  of  the  Institution  of  Civil  Engineers, 
vol.  113,  pp.  194-216.) 

Describes  test  apparatus  and  its  operation,  and  presents  data 
obtained  in  tests  of  several  different  types  of  governors. 

53.  RATEAU,  A.    Les  Turbo-machines.    1900.    (In  Revue  de  Mecanique, 

vol.  6,  pp.  393-441,  539-561.) 

Being  "Ch.  V.  Regularisation  automatique  de  la  Vitesse  des 
Turbines"  of  a  longer  serial  on  turbines  in  general. 

Contains  material  on  the  construction  of  governors,  but  is 
principally  concerned  with  the  theory  of  governing. 

54.  RAUSER.     Ueber  Regler  fur   Dampfmaschinen   bei   Gassaugeran- 

lagen,  Bauart  Pintsch.  1902.  (In  Journal  fur  Gasbeleuchtung 
und  Wasserversorgung,.vol.  45,  pp.  89-90.) 

The  same,  abstract  translation.  1902.  (In  Journal  of  Gas 
Lighting,  Water  Supply,  etc.,  vol.  79,  p.  964.) 

Description  of  construction  and  operation  of  Pintsch's  ex- 
hauster engine  governor. 

55.  REICHEL,  E.     Die  Weltausstellung  in  Paris,  1900;    Turbinenbau. 

1900-1901.     (In  Zeitschrift  des  Vereines  Deutscher  Ingenieure, 


226      GOVERNORS  AND  THE  GOVERNING  OF  PRIME  MOVERS 

vol.  44,  pt.  1,  pp.  657-659;  vol.  44,  pt.  2,  pp.  1113-1118,  1348- 
1359;  vol.  45,  pt.  2,  pp.  1386-1393,  1562-1567,  1631-1636, 
1837-1842.) 

Contains  material  giving  descriptions  and  illustrations  of 
several  types  of  turbine  governors. 

56.  REPLOGLE,  M.  A.    Some  Stepping  Stones  in  the  Development  of 

a  Modern  Water-wheel  Governor.  1906.  (In  Transactions  of 
the  American  Society  of  Mechanical  Engineers,  vol.  27, 
pp.  642-660.  Discussion,  pp.  660-661.) 

Treats  of  the  fundamental  requisites  which  must  be  met  by 
the  governor,  and  tells  how  these  requisites  may  be  attained. 

57.  RILEY,  J.  C.     Apparatus  for  Obtaining  a  Continuous  Record  of 

the  Position  of  an  Engine  Governor  and  the  Speed  of  the  Engine 
Which  it  is  Governing.  1903.  (In  Transactions  of  the  American 
Society  of  Mechanical  Engineers,  vol.  24,  pp.  78-97.)  Describes 
construction  and  operation  of  instrument. 

"Bibliography  of  Experimental  Work  on  Engine  Governors," 
pp.  96-97. 

r.   RITES,  F.  M.    Analysis  of  the  Shaft  Governor.    1893.    (In  Transac- 
tions of  the  American  Society  of  Mechanical  Engineers,  vol.  14, 
pp.  92-113.    Discussion,  pp.  114-117.) 
Theoretical  treatment. 

59.  SCHNEIDER,  O.     Theorie  der  Flachregler.     1895.     (In  Zeitschrift 

des  Vereines  Deutscher  Ingenieure,  vol.  39,  pt.  2,  pp.  1256-1261, 
1288-1292.) 
Theoretical  treatment. 

60.  SEARING,  E.  D.    Analysis  of  Water-wheel  Governor  Effort.    1915. 

(In  Proceedings  of  National  Electric  Light  Association,  38th 
convention,  San  Francisco,  June,  1915,  pt.  2,  pp.  468-493.) 

Gives  methods  for  determining  governor  effort  in  plants  under 
operation. 

61.  SIEMENS,    C.    W.      Description    of    an    Improved    Chronometric 

Governor  for  Steam  Engines,  etc.  1866.  (In  Proceedings  of 
the  Institution  of  Mechanical  Engineers,  vol.  17,  pp.  19-31. 
Discussion,  pp.  32-42.) 

62.  SIEMENS,  C.  W.     On  an  Improved  Governor  for  Steam  Engines. 

1853.  (In  Proceedings  of  the  Institution  of  Mechanical  Engineers, 
vol.  4,  pp.  75-83.  Discussion,  pp.  83-87.) 

Illustrated  description  of  several  of  the  earlier  types  of 
governors,  with  special  attention  to  the  author's  "  Chronometric 
Governor." 


BIBLIOGRAPHY  227 

63.  SMITH,  J.  M.    Governor  for  Steam  Engines.     1890.     (In  Transac- 

tions of  the  American  Society  of  Mechanical  Engineers,  vol.  11, 
pp.  1081-1087.  Discussion,  pp.  1087-1101.) 

Treats  of  the  design  and  theory  of  a  new  type  of  shaft  governor. 

64.  SPARRE,  COMTE  DE.    Note  au  Sujet  de  la  Theorie  des  Re*gulateurs. 

1903.     (In  Revue  de  Mecanique,  vol.  12,  pp.  558-560.) 

Comment  on  paper  by  L.  Lecornu,  Mathematical  treatment. 
See  also  reply  by  L.  Lecornu,  pp.  560-561. 

65.  STODOLA,  A.    Das  Siemenssche  Regulierprinzip  und  die  Amerika- 

nischen  "  Inertie-regulatoren."    1899.    (In  Zeitschrift  des  Vereines 
Deutscher  Ingenieure,  vol.  43,  pt.  1,  pp.  506-516,  573-579.) 
Theoretical  treatment. 

66.  STODOLA,  A.    Die  Dampfturbinen  und  die  Aussichten  der  Warme- 

kraftmaschinen;  Versuche  und  Studien.  Ed.  4,  enl.  1910. 
Julius  Springer,  Berlin. 

Governors  considered,  pp.  335-356.     Technical  in  treatment. 

67.  STODOLA,  A.     Die  neue  hydraulische  Regelung  der  Sulzerdampf- 

turbine  und  Versuche  an  der  2000  K.W.-turbine  des  Easier 
Elektrizitatswerkes.  1911.  (In  Zeitschrift  des  Vereines 
Deutscher  Ingenieure,  vol.  55,  pt.  2,  pp.  1709-1716,  1794-1800, 
1846-1852.) 

Profusely  illustrated,  and  practically  nonmathematical  in 
treatment. 

68.  STRNAD,F.  Neuere  Geschwindigkeitsregler.  1907.  (In  Zeitschrift  des 

Vereines  Deutscher  Ingenieure,  vol.  51,  pt.  1,  pp.  23-28,  62-67.) 
Concerned  principally  with  illustrated  descriptions  of  apparatus. 

69.  STURGESS,  J.     Speed  Regulation  of  Water-power  Plants.     1906. 

(In  Transactions  of  the  American  Society  of  Mechanical  En- 
gineers, vol.  27,  pp.  682-697.) 

Treats  of  the  fundamental  requisites  of  successful  speed  regu- 
lation. Gives  data  showing  how  these  requisites  are  met  in 
various  plants  under  operation. 

70.  SWEET,  J.  E.     Effect  of  an  Unbalanced  Eccentric  or  Governor 

Ball  on  the  Valve  Motion  of  Shaft-governed  Engines.     1890. 
(In  Transactions  of  the  American  Society  of  Mechanical   En- 
gineers, vol.  11,  pp.  1053-1055.     Discussion,  pp.  1055-1067.) 
Principally  theoretical  in  treatment. 

71.  THOMA.    Die  neuen  Turbinenregler  von  Briegleb,  Hansen  &  Co., 

in  Gotha.     1912.     (In  Zeitschrift  des  Vereines  Deutscher  In- 
genieure, vol.  56,  pt.  1,  pp.  121-127,  169-175.) 
Nonmathematical. 


228      GOVERNORS  AND  THE  GOVERNING  OF  PRIME   MOVERS 

72.  TOLLE,  M.    Beitrage  zur  Beurteilung  der  Zentrifugalpendelregu- 

latoren.    1895-1896.    (In  Zeitschrift  des  Vereines  Deutscher  Inge- 
nieure,  vol.  39,  pt.  1,  pp.  735-741,  776-779;   vol.  39,  pt.  2,  pp. 
1492-1498,  1543-1551;  vol.  40,  pt.  2,  pp.  1424-1428,  1451-1455.) 
Theoretical  treatment. 

73.  TOLLE,  M.    Die  Regelung  der  Kraftsmaschinen;  Berechnung  und 

Konstruktion  der  Schwungrader,  des  Massenausgleichs  und  der 
Kraftmaschinenregler  in  elementarer  Behandlung.  Ed.  2,  re- 
vised and  enl.,  699  pages.  1909.  Springer,  Berlin. 

Governors  considered,  pp.  275-699.  Comprehensive  treat- 
ment of  design  and  operation.  Considerable  mathematical 
theory  included. 

74.  THINKS,  W.  and  HOUSUM,  C.    Shaft  Governors.    97  pages.  1905. 

Van  Nostrand.     (Van  Nostrand  Science  Series.) 

Mathematical  discussion  of  the  forces  to  be  considered  in 
their  design.  Considers  only  the  statics  of  shaft  governing. 

75.  TURBO-BLOWER  GOVERNING  DEVICES.     1915.     (In  Journal  of  the 

American  Society  of  Mechanical  Engineers,  vol.  37,  pp.  181-182.) 
Illustrated  abstract  translation  of  part  of  a  serial  article  on 
"Die  Dampfturbinen  und  die  Turbogeblase  an  der  Schweiz," 
by  A.  Stodola,  in  Schweizerische  Bauzeitung,  vol.  65,  p.  24, 
Jan.  16,  1915. 

76.  UHL,  W.  F.     Speed  Regulation  in  Hydro-electric  Plants.     1912. 

(In  Transactions  of  the  American  Society  of  Mechanical  En- 
gineers, vol.  34,  pp.  379-432.  Discussion,  pp.  433-434.) 

Includes  much  theoretical  material.  Presents  an  appendix 
containing  tables  of  useful  data. 

77.  WAGENBACH,  W.    Fortschritte  im  Bau  der  Wasserturbinen,  zugleich 

Bericht  iiber  die  Schweizerische  Landesausstellung  in  Bern,  1914- 
1915.  (In  Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  59, 
pt.  2,  pp.  937-941,  955-962,  997-1002,  1018-1024,  1054-1057.) 

Contains  considerable  on  governors  for  hydraulic  turbines. 
Well  illustrated  and  nonmathematical. 

78.  WARREN,  H.  E.     Speed  Regulation  of  High  Head  Water-wheels. 

1907.  (In  Technology  Quarterly,  vol.  20,  pp.  187-208.) 
Discusses  fundamentals  of  speed  regulation,  giving  some  theory 

and  outlining  test  methods  for  ascertaining  the  regulation  of 
wheels  under  operation. 

79.  WHITE,  W.  M.  and  MOODY,  L.  F.    Glocker- White  Turbine  Governor. 

1908.  (In  Power  and  the  Engineer,  vol.  29,  pp.  201-205.)    Ex- 
planation of  the  principle  of  this  water-wheel  governor. 


BIBLIOGRAPHY  229 

80.  WOODS,  J.    Chronometric  Governor.     1846.     (In  Minutes  of  Pro- 

ceedings of  the  Institution  of  Civil  Engineers,  vol.  5,  pp.  255-261. 
Discussion,  pp.  261-265.) 

Describes  the  method  of  operation  of  the  chronometric  gov- 
ernor invented  by  E.  W.  and  C.  W.  Siemens. 

81.  WUNDERLICH,  H.    Ncuere  Fortschritte  im  Bau  von  Turbogeblasen 

und  Turbokompressoren.     1915.     (In  Zeitschrift   des  Vereines 
Deutscher  Ingenieure,  vol.  59,  pt.  1,  pp.  129-135,  174-181.) 

Contains  considerable  on  governors  for  turbo-blowers.    Non- 
mathematical  in  treatment. 

82.  BAUERSFELD,  W.     Ueber  die  automatische  Regulierung  der  Tur- 

binen.     1905.     Berlin. 

Relay  governors  —  theoretical  treatment. 

83.  RULF,  B.    Der  Reguliervorgang  bei  Dampfmaschinen.    1902.    (In 

Zeitschrift  des  Vereines  Deutscher  Ingenieure,  vol.  46,  pt.  2, 
pp.  1307-1314,  1399-1403.) 
Graphical  method  of  determining  speed  change. 


INDEX 


Actual  motion  of  governor,  81 

Addition  of  constant  force  at  sleeve,  37 

Additional  power-control  mechanism, 
201 

Adjustment  of  equilibrium  speed,  49 
of  rate  of  flow,  151 
of  static  fluctuation,  180 

Adjustments  in  shaft  governors,  76 

Amplitude,  maximum  permissible,  86 
of  first  speed  wave,  96 
of    vibration    due    to    impressed 
force,  87,  217 

Angular  displacement  from  curve  of 
impressed  moments,  217 

Anti-racing  device,  176 

Armstrong  governor  with  compensat- 
ing oil  pot,  111 

Assembly  drawing,  relay  governor,  183 

Automatic    disconnecting    device   for 
capacity  governor,  58 

Auxiliary  governor,  145 

Auxiliary  spring,  200 

B 

Balanced  regulating  valve,  38 

Bee  governor,  109 

Belt  slip  a  cause  of  racing,  198 

Binding  due  to  lack  of  alignment,  197 

Brake  resistance  traversing  time,  133 


Capacity  of  oil  pump,  relay  governing, 
185 

Cataract  governors,  143 

Centrifugal  compensator,  144 
force,  7 
force,     equivalent,    for     oblong 

weights,  41 

mass,  size  of,  in  shaft  governors,  72 
moment  of  eccentric  and  strap,  64 
moment  of  oblong  weights,  214 


moment  of  rotating  masses,  shaft 

governors,  63 
Change  gears,  50 

of  angle  of  characteristic,  29 

of  pressure,  accumulated  effect  of 

speed  change,  153 
of  spring  tension  and  leverage, 

shaft  governors,  75 
Changing  lever  arm  and  initial  tension, 

54 

Character  of  regulation,  factors  deter- 
mining, 132 
Characteristic,  characteristics 

curves  of  governors,  26,  52,  214 
detail  construction  of,  214 
of  displacement  pumps,  156 
of  Hartnell  type  governor,  36,  52 
of  isochronous  governor  with  ob- 
long weights,  43 
of  Proell  type  governor,  35 
of  turbo-compressor,  156 
Chorlton-Whitehead  governor,  109 
Chronometric  governor,  141 
Close  regulation,  21 
Closeness  of  regulation,  pressure  gov- 
erning, 153 
Combination  centrifugal  and  pressure 

governor,  167,  168 
hydraulic  and  mechanical  relay 

governor,  173 
Compensating  oil  pot,  shaft  governors, 

111 

return,  176 
Compensator,  179,  195,  199 

friction  wheel,  183 

Compound  centrifugal  forces,  14,  118 
Constant  delivery  compared  with  con- 
stant speed,  148 

force  at  sleeve,  addition  of,  37,  38 
rate  of  flow  governing,  148 
solid  friction,  cause  of  vibrations, 
123 


231 


232 


INDEX 


Coriolis'  forces,  14,  118 
Cosine  governor,  xvi 
Criterion  of  stability,  25 
Cut-off  control,  lack  of  stability,  155 
Cyclical  vibrations  of  governors,  85 
eliminate  friction,  87 


Detail  construction  of  characteristic, 

214 

Detention  by  friction,  15,  209 
due  to  forces  at  collar,  55 
eliminated  by  vibration,  16 
importance  in  relay  governors,  171 
Diagram  of  vibration,  125 
Direct-control  governors,  3 

limits  of,  170 
Discarded  types  of  speed  governors, 

139 

Distribution  of  forces  between  eccen- 
tric and  strap,  68 
of  mass  in  governors,  84 
Displacement  pumps,  automatic  sta- 
bility, 154 

characteristics  of,  156 
Double  floating  relay  valve,  182 
relay,  181 

Dust  and  tar  in  gas,  171 
Dynamic  action  of  steam  flow,  170 

regulating  force,  102 
Dynamometric  governors,  141 


E 

Eccentriq  and  strap,   force  distribu- 
tion, 68 
Effect   of   adding   constant   force   at 

sleeve,  38 
of   outside   forces   impressed   on 

governor,  81 
of  valve  inertia,  66 
Electrical  governor,  146 
Energy  released  by  governor,  173 

beyond  control  of  governor,  201 
Equation  of  motion  of  governor  mass, 
133 


Equilibrium  speed,  23 
adjustment  of,  49 

Equivalent  centrifugal  force  with  ob- 
long weights,  41 
friction,  18 
mass  of  governor  parts,  46,  48,  78, 

84,  117,  132 

static  fluctuation,  114,  115 
Erratic  behavior  of  shaft  governors,  67 
Experimental  determination  of  gov- 
ernor's strength,  5 


Floating  relay  valve,  182 

Flywheel  effect  not  great  enough,  201 
weight  per  horsepower,  111,  199 

Force,  Forces 

acting  on  governor  sleeve,  37 
on  collar,  variation  of,  50,  51 
outside,  impressed  on  governor,  81 
required  for  damping  vibrations, 
103 

Fraction  of  load  suddenly  applied,  106 

Friction 

a  cause  of  racing,  196 
between  eccentric  and  strap,  67 
detention  by,  15,  55,  209 
drive  of  governors,  51 
eliminated  by  cyclical  vibrations, 

87,  203 

eliminated  by  impressing  vibra- 
tion, 171 

harmful  in  pressure  governing,  166 
increases  resistibility,  83 
influence  in  relay  governors,  192 
internal,  18 

moment,  shaft  governors,  68 
of    compound    centrifugal   force, 

118;    not  adjustable,  119 
of  governor  collar,  55 
of  joints,  210 
of  pilot  valve,  186 
of  valve  gear,  shaft  governors,  66 
of  working  fluid  of  prime  movers, 

204 
wheel  compensation,  183 

Frictionless   governor,  regulation  im- 
possible with,  101 


INDEX 


233 


Gas  engines,  regulation  of,  21 
General   Electric   Co.'s  volume   gov- 
ernor, 150 
Governing,  for  constant  rate  of  flow, 

148 

for  constant  pressure,  153 
of  hydraulic  turbines  with  long 

supply  lines,  172,  178 
principles  of,  2 
Governor,  governors 
as  a  mechanism,  28 
as  speed  counters,  25 
displacement  proportional  to  load 

change,  136 

too  light  for  vibratory  forces,  202 
too  small,  202 
troubles  and  remedies,  195 
vibrates,  jerks,  202 
with  considerable  internal  friction, 

21 

with  small  internal  friction,  21 
Greatest  speed  variation,  96,  128 
limiting  case,  103,  104 
estimated  from  limiting  case,  137 

H 

Harmonic  vibrations  of  limiting  case, 

103 
Hartnell  type  governor,  characteristic, 

36 

Helical  spring  stiffness,  changing,  195 
Hydraulic  (cataract)  governor,  143 
turbines  with  long  supply  lines, 
173,  178 

I 

Impressed  forces  keep   governor  vi- 
brating, 71 

Inertia  governors,  9,  11 
moment,  13 
moment   of   reciprocating   parts, 

shaft  governors,  64 
(tangential)  in  shaft  governors,  71 
Influence  of  friction  in  relay  governing, 

192 
of   throttling   in   non-condensing 

engines,  205 

Ingersoll-Rand  volume  governors,  150 
Insufficient  size  of  governor,  202 


Interaction    between    governor    and 

prime  mover,  95 

Internal  combustion  engines,  self -regu- 
lating properties,  206 
governor  friction,  18,  20 
Inverted   suspension   type   governor, 

characteristic,  35 
Isochronous  governor,  xvi,  24 
characteristic,  43 
impracticability  of,  108 
with  tangential  inertia,  116 


Knife  edge  joints,  171 

edges,  in  releasing  gears,  197 
edges  wear  too  fast,  203 

Knowles  compensator,  144 


Lag  of  governor  motion  behind  speed 
change,  129 

Lap  of  pilot  valve,  193 

Large  pilot  valves,  effect  of,  176 

Leakage  in  pilot  valve,  197 

Limitations  of  volume  governing  in 
blast-furnace  practice,  152 

Limiting  case,  97 

greatest  speed  fluctuation,  104 
harmonic  vibrations,  103 
pressure  regulation,  159 
relative  speed  fluctuation,  108 
with  solid  friction,  120 

Limits  of  direct-control  governors,  170 

Load  governors,  141 

Lost  motion,  eliminated,  183 

in  joints,  relay  governing,  193, 197 

M 

Mass,  equivalent,  effect  of,  84 
distribution  in  governors,  84 
of  governor  parts,  46 
of  governor  springs,  influence  of, 

73 

Maximum  permissible  amplitude,  86 
Minimum  spring  scale  for  stability,  162 
Moment  due  to  friction  between  ec- 
centric and  strap,  67 
due  to  friction  of  valve  gear,  66 
due   to   inertia   of   reciprocating 
parts,  64 


234 


INDEX 


Natural  period  of  vibration  of  governor, 

77 

in  relay  governing,  191 
Nordberg  governor,  59 


Oblong     swinging     weights     reduce 

promptness,  44 

weights,  centrifugal  moment,  214 
Oil  as  fluid  for  relay  governors,  173 
Oil  gag  pot,  103,  105,  196 

compensating,  in  shaft  governors, 

111 

in  pressure  governing,  164 
size  of,  113 
with  floating  springs,   109,   195, 

199,  200 

Outside  forces  impressed  on  governor, 
81 


Parabola  of  speed  deviation,  188 
Parallel  operation  of  A.  C.  generators, 
116,  179 

of  compressors  and  blowers,  167 
Parsons  system  of  puff  governing,  171 
Passive  resistance,  18 
Pilot  valve,  174,  185,  186 

can  overtravel,  191 

lap,  193 

leakage,  197 

Positive  displacement  pumps,  148 
Pressure  governing,  153 

effect  of  friction,  166 

limiting  case,  159 

minimum  spring  scale,  162 

oil  gag  pot  in,  164 

speed  damping,  165 

traversing  time,  163 

without  receivers  for  intake  and 

discharge,  165 

Principles  of  relay  governing,  174 
Process  of  regulation,  180 
Proell  type  governor,  characteristic,  21 
Promptness,  44,  45,  195,  199 
Puff  governing,  171 
Pump  governors,  143 


R 

Racing,  195,  196,  198 

caused  by  absence  of  a  return,  re- 
lay governors,  199 
caused  by  friction  in  governor  or 

relay,  196,  197 

caused  by  incorrect  throttle  con- 
trol, 200 

caused  by  releasing  gears,  197 
caused  by  slipping  belt,  198 
caused  by  valve  adjustments,  196 
of    centrifugal  pumps  and  blow- 
ers, 201 

point,  shaft  governors,  76 
Rateau  multiplier,  150 
Rateau  volume  governor,  150 
Reciprocating  valves,  inertia  of,  66 
Regulating  force,  7 
dynamic,  102 
equation,  derivation,  209 
static,  102 

Regulating  moment  of  tangential  in- 
ertia, 9 

valve,  balanced,  38 
Regulation  by  frictionless  governors, 

101 
Regulation  not  close  enough,  195 

of  gas  engines  with  dirty  gas,  21 
Relative  change  of  governor  position, 

130 

change  of  load,  100 
change  of  speed,  130 
speed  fluctuation,  limiting  case, 

108 

Relay,  double,  181 
governing,  170 
governing,    effects    of    governor 

mass,  172 

governing,  principles  of,  174 
governor,  3 

governor,  assembly  drawing,  183 
governor,  effect  of  friction  in,  171 
governor,  influence  of  static  fluc- 
tuation, 190 
governor,   lost  motion  in  joints, 

193,  197 
governor,  relative  speed  change, 

189 
governor,  theory,  186 


INDEX 


235 


governor,  variable  relay  velocity, 
194 

governor,  with  rigid  return,  175, 
176 

governor,  without  return,  175 

governor,  work  capacity,  184,  185 

mechanisms,  173 

traversing  time,  172 

valve,  floating,  182 

with  slowly  yielding  return,  178 
Representative  point,  98 
Resistibility,  81 

increased  by  friction,  83 
Reversed  speed  curve,  116,  180,  181 


Safety  device  to  prevent  overspeeding, 

168 

Self -regulating  features  of  prime  mov- 
ers, 204 

of  the  load,  204,  207 
Sensitiveness,  24 

no  guarantee  for  close  regulation, 

25 
Shaft  governors,  5,  10,  61 

adjustment  of,  75 

calculation  of,  62 

compensating  oil  pot  in,  111 

erratic  behavior  of,  67 

friction  moment,  68 

inertia  moment  of  reciprocating 
parts,  64 

influence  of  tangential  inertia  in, 
71,  85 

spring  moment,  69 

unbalanced  weights,  89 
Shape  of  centrifugal  weights,  40 
Siemens'  principle,  140 
Sluggishness,  15 

Solid  friction,  as  damping  agent,  117, 
118,  123,  124,  127 

limiting  case,  120 

minimum  static  fluctuation,  121 

for  damping  vibrations,  83 
Speed  counter,  23,  25 
Speed  damping,  165 
Speed  fluctuation,  excessive,  201 

greatest,  128 

limiting  case,  103,  104 


Speed  limit,  centrifugal  governors,  167 
Speed  of  relay  mechanism,  187 
Speed  restorer,  179 

Speed  rise  due  to  energy  beyond  con- 
trol, 137 
Speeder,  54 
Spindle  governors,  10 
Spring  in  oil  gag  pot,  200 
Spring  leverage,  change  of,  75 
Spring  moment,  69 
Spring  stiffness,  changing,  195 
Spring  tension,  change  of,  75 
Springs,  influence  of  mass  of,  73 
Stability,  23,  29,  31,  32 

found  from  characteristic,  31 

of  regulation,  33,  96, 151,  154 

of  regulation,  enforced  by  oil  pot, 
105 

of  regulation,   influence  of  tan- 
gential inertia  on,  113 

temporary,  by  compensating  dash- 
pots,  164,  178 
Starting  time,  107 

of  inertia  mass,  133 
Static  fluctuation,  23,  32 

equivalent,  114,  115 

minimum  with  solid  friction,  121, 
122 

negative,  116,  180 

pressure  governing,  164 

reduced  by  tightening  spring,  52 
Static  regulating  force,  102 
Static  speed  fluctuation  of  regulating 

mechanism,  177 
Steam  relay  pistons,  173 
Stodola's  theory  of  relay  governing, 

186 

Strength,  experimental  determination 
of,  5 

of  centrifugal  governors,  4 

of  volume  governors,  150 


Tangential  inertia,  8,  195 
in  shaft  governors,  71, 85 
influence  upon  stability  of  regula- 
tion, 113,  116 

Temporary  stability,  compensating  oil 
pot,  164,  178,  180 


236 


INDEX 


Thompson  governor,  73 

Throttle  control,  inherent  stability  of, 

155,  205 

Total  inertia  moment,  13 
Traversing  time,  45 

brake  resistance,  133 

calculation  of,  47 

of  relay,  172 

pressure  governing,  163 
Turbo-blower,  characteristics,  157 

surging  of,  157 

U 
Unbalanced    forces    impressed    upon 

governors,  39 
Unbalanced  weights  in  shaft  governors, 

89 
Unloading  devices,  158 


Vane  governors,  144 

Valve  adjustments,  racing  caused  by, 

196 

Variable  speed  governors,  49 
Velocity  pumps,  148 


Vibrating  weight,  path  of,  91 
Vibration  diagram,  125 

effect  upon  governor  friction,  16, 
203 

natural  period  of,  77 
Vibrations,  cyclical,  86,  86 

harmonic,  103 

limited  by  governor  resistibility, 

82 
Volume  governors,  150 

W 

Watt  governor,  xvi,  78 

Watt   type    governor,    detention    by 
friction,  209 

Watt's  principle,  139 

Weight  of  flywheel  required  per  horse- 
power, 111,  199 

Weiss  governor,  59 

Wischnegradsky's  theorem,  101 

Woodward  governor,  183 

Work  capacity,  centrifugal  governors, 

14,33 
relay  governors,  184 

Work  done  by  steam  beyond  governor 
control,  138 


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